Methods for modeling risk situations. Risk theory and modeling of risk situations - A. Shapkin
When managing risk, it is often necessary to compare real situations with hypothetical ones (what would happen if everything went differently). This dramatically complicates the analysis of risk situations, since it requires a basis for studying and measuring what was not. Currently, to describe such hypothetical situations, there is no other way than to use mathematical models called models of risk situations. This is the basis for quantitative risk management. Its essence consists in the application of economic and mathematical models for predicting situations characterized by risk and uncertainty, and the justification of appropriate management decisions.
A model is a simplified description of a real object or process that focuses on properties important to the researcher and ignores those aspects that seem to the researcher to be insignificant. The main difficulty of modeling consists in finding out which properties are considered important and which are not. The correct description of important properties ensures the adequacy of the model, and the correct choice of secondary, ignored properties helps to sufficiently simplify such a representation. The model should serve as a decision-making tool, that is, it should clarify for the decision-maker how the process can develop, what outcomes will take place, and suggest various actions (for example, to prevent damage).
The most important class of models used in risk management are mathematical models. They allow you to describe the essential aspects of the studied process or phenomenon in the form of mathematical relationships, and then analyze them using the appropriate mathematical apparatus. It is especially important to use mathematical models to predict alternatives for future development. This is what allows the manager to quantify the future consequences of decisions.
The mathematical models used in risk management are very diverse and diverse. Such a concept as a universal model does not exist. The multiplicity of types of risks and the variety of mechanisms for their occurrence make this impossible. In different situations, we will use specific tools (in this case, models), because each model is unique in its own way, since when building it, you should start from the properties of the modeling object itself. However, similar situations allow us to use similar (if not the same) tools: there are some general approaches to modeling (for example, the use of stochastic differential equations or another mathematical apparatus). If a more or less standard approach can be applied, then the modeling process will be simpler (approaches to building a model and obtaining a solution are known).
In the field of quantitative risk management, probabilistic and statistical models are most common.
For some types of risks, the widespread use of mathematical models is standard, for others it is not yet. Nevertheless, there is an intensive development of various modeling techniques using risk management features. Quantitative risk management is becoming a separate “branch” of risk management.
Title: Risk theory and modeling of risk situations.
The textbook outlines the essence of uncertainty and risk, classification and factors acting on them; methods of qualitative and quantitative assessment of economic and financial situations in conditions of uncertainty and risk are given.
The classification of service technologies is given, examples of the activities of service organizations in risk situations are considered.
The methodology of managing investment projects in risk conditions is described, recommendations are given on managing the investment portfolio, an assessment is made of the financial condition and development prospects of the investee, and a model for accounting risks in investment projects is proposed.
Considerable attention is paid to management methods and models in conditions of risk and psychology of behavior and assessment of a decision maker.
For students and graduate students of economic universities and faculties, students of business schools, risk managers, managers of innovations, investments, as well as specialists in banking and financial institutions, employees of pension, insurance and investment funds.
Content
Foreword
Chapter 1 PLACE AND ROLE OF ECONOMIC RISKS IN THE MANAGEMENT OF ORGANIZATIONS
1.1. Organizations, types of enterprises, their characteristics and goals
1.2. The place and role of risks in economic activity
1.2.1. Definition and nature of risks
1.2.2. Management of risks
1.2.3. Risk classification
1.2.4. Uncertainty system
1.3. Risk management system
1.3.1. Management activities
1.3.2. Risk management
1.3.3. Risk management process
1.3.4. Mathematical methods for assessing economic risks
Chapter 2 RISKS OF SERVICE SPHERES
2.1. Service Technology
2.2. Risk classification of service enterprises
2.3. Dynamic analysis of the situation in the service market
2.4. Service Risk Management Model
Chapter 3 EFFECT OF MAJOR MARKET EQUILIBRIUM FACTORS ON RISK MANAGEMENT
3.1. Risk limitation factors
3.2. The influence of market equilibrium factors on risk change
3.2.1. The relationship of market equilibrium and commercial risk
3.2.2. The influence of market equilibrium factors on changes in commercial risk
3.2.3. Modeling the process of achieving equilibrium
3.2.4. The impact of changes in demand on the level of commercial risk
3.2.5. The impact of supply changes on the degree of commercial risk
3.2.6. Building demand dependencies on supply
3.3. Effect of time factor on risk
3.4. The influence of elasticities of supply and demand on the level of risk
3.5. The effect of tax factor in market equilibrium on the level of risk
Chapter 4 FINANCIAL RISK MANAGEMENT
4.1. Financial risk
4.1.1. Classification of financial risks
4.1.2. The relationship of financial and operational leverage with aggregate risk
4.1.3. Development risks
4.2. Interest rate risks
4.2.1. Types of interest rate risks
4.2.2. Interest operations
4.2.3. Percent Average
4.2.4. Variable interest rate
4.2.5. Interest rate risks
4.2.6. Bonds Interest Risk
4.3. The risk of losses from changes in the flow of payments
4.3.1. Equivalent Streams
4.3.2. Payment streams
4.4. Risky investment processes
4.4.1. Investment risks
4.4.2. Risky asset return rates
4.4.3. Net present value
4.4.4. Annuity and repayment fund
4.4.5. Investment Valuation
4.4.6. Risky Investment Payments
4.4.7. Discount over time
4.5. Credit risk
4.5.1. Credit risk factors
4.5.2. Credit Risk Analysis
4.5.3. Credit risk mitigation techniques
4.5.4. Loan payments
4.5.5. Increase and payment of interest in consumer credit
4.5.6. Loan guarantees
4.6. Liquidity risk
4.7. Inflation risk
4.7.1. The relationship of interest rates with inflation
4.7.2. Inflation premium
4.7.3. Influence of inflation on various processes
4.7.4. Measures to Reduce Inflation
4.8. Currency risks
4.8.1. Currency Conversion and Interest Increase
4.8.2. Exchange rates over time
4.8.3. Currency risk reduction
4.9. Asset Risks
4.9.1. Exchange Risks
4.9.2. Effect of default risk and asset value taxation
4.10. Probabilistic assessment of the degree of financial risk
Chapter 5 QUANTITATIVE ASSESSMENTS OF ECONOMIC RISK UNDER UNCERTAINTY
5.1. Methods for making effective decisions in the face of uncertainty
5.2. Matrix games
5.2.1. The concept of a game with nature
5.2.2. The subject of game theory. Basic concepts
5.3. Performance Criteria Under Uncertainty
5.3.1. Guaranteed Result Criterion
5.3.2. Optimism criterion
5.3.3. Criterion of pessimism
5.3.4. Savage minimax risk criterion
5.3.5. The criterion of generalized maximin (pessimism - optimism) Hurwitz
5.4. Comparative evaluation of solution options depending on performance criteria
5.5. Multicriteria problems of choosing effective solutions
5.5.1. Multi-criteria tasks
5.5.2. Pareto Optimality
5.5.3. Choice of solutions with multi-criteria alternatives
5.6. Partial Uncertainty Decision Making Model
5.7. Determining the optimal volume of clothing production in the face of uncertainty
5.7.1. Upper and lower price of the game
5.7.2. Reduction of a matrix game to a linear programming problem
5.7.3. Selection of the optimal product range
5.8. Risks associated with the operation of the sewing enterprise
Chapter 6 ADOPTION OF THE OPTIMUM DECISION IN THE CONDITIONS OF ECONOMIC RISK
6.1. Probabilistic statement of making preferred decisions
6.2. Risk assessment under certainty
6.3. The choice of the optimal number of jobs in the hairdresser, taking into account the risk of service
6.4. Statistical decision-making methods in risk
6.5. Choosing the optimal plan by building event trees
6.5.1. Decision tree
6.5.2. Market entry strategy optimization
6.5.3. Maximizing stock returns
6.5.4. Selection of the optimal dry cleaning factory reconstruction project
6.6. Benchmarking Solution Options
6.6.1. Choosing the best solution using statistical estimates
6.6.2. Normal distribution
6.6.3. Risk curve
6.6.4. Choosing the optimal solution using confidence intervals
6.6.5. Production Cost Forecasting Model
6.7. The occurrence of risks in setting the mission goals of the company
6.8. Activities of service enterprises at risk
6.8.1. Company for decoration and design. Bakery products and their subsequent sale
6.8.3. Beauty saloon
Chapter 7 RISK MANAGEMENT OF INVESTMENT PROJECTS
7.1. Investment projects in conditions of uncertainty and risk
7.1.1. Basic concepts of investment projects
7.1.2. Analysis and evaluation of investment projects
7.1.3. Risks of investment projects
7.2. Optimal choice of investment volume, providing maximum output growth
7.3. Investment in a portfolio of securities
7.3.1. Investment management process
7.3.2. Diversified portfolio
7.3.3. Risks associated with investing in a securities portfolio
7.3.4. Practical recommendations for the formation of an investment portfolio
7.4. Analysis of the economic efficiency of the investment project
7.4.1. Analysis of Concomitant Risk Factors
7.4.2. Preliminary assessment and selection of enterprises
7.4.3. Assessment of the financial condition of the enterprise as an object of investment
7.4.4. Examples of analysis using financial ratios
7.4.5. Assessment of the development prospects of the organization
7.4.6. Comparative financial analysis of investment projects
7.4.7. Analysis of site survey methods
7.5. Risk accounting in investment projects
7.5.1. Project Risk Assessment Model
7.5.2. Risk accounting when investing
7.5.3. Practical conclusions on managing risky investment projects
Chapter 8 TOURISM RISK MANAGEMENT
8.1. Factors affecting the dynamics of tourism development
8.1.1. Tourism Development in Russia
8.1.2. Types and forms of tourism
8.1.3. Features of tourism - as factors of development uncertainty
8.2. Psychology of the impact of tourism on participants and others
8.2.1. Travel motivation
8.2.2. Impact of tourism
8.3. Risks associated with tourism activities
8.3.1. Factors Affecting Tourism and Tourism Economics
8.3.2. Tourism risk classification
8.4. The economic impact of tourism
8.5. Managerial decision making
8.6. Analysis of the activities of the organization for the provision of tourism services at risk
Chapter 9 RISK-MANAGEMENT OF HOTELS AND RESTAURANTS
9.1. Hotel business development
9.2. Factors in the development of the restaurant business
9.3. Features and specifics of hospitality
9.4. Risks inherent in the hospitality industry and their management
9.4.1. Risk identification
9.4.2. Risks of investment projects
9.4.3. Hospitality industry risk reduction
9.5. Hospitality Management Solutions
Chapter 10 BASIC METHODS AND WAYS TO REDUCE ECONOMIC RISKS
10.1. General risk management principles
10.1.1. Risk Management Process Diagram
10.1.2. Risk Examples
10.1.3. The choice of risk management techniques
10.2. Diversification
10.3. Risk insurance
10.3.1. The essence of insurance
10.3.2. Key Features of Insurance Contracts
10.3.3. Calculation of insurance operations
10.3.4. Insurance contract
10.3.5. Advantages and disadvantages of insurance
10.4. Hedging
10.4.1. Risk management strategies
10.4.2. Basic concepts
10.4.3. Forwards and futures contracts
10.4.4. Exchange rate hedging
10.4.5. Key Risk Aspects
10.4.6. Swap rate hedging
10.4.7. Options
10.4.8. Insurance or hedging
10.4.9. Cash flow synchronization
10.4.10. Hedging model
10.4.11. Hedge Performance Measurement
10.4.12. Minimize Hedge Costs
10.4.13. Correlated Hedge Operation
10.5. Limitation
10.6. Reservation of funds (self-insurance)
10.7. Quality risk management
10.8. Acquisition of additional information
10.9. Assessment of the effectiveness of risk management methods
10.9.1. Risk financing
10.9.2. Assessment of the effectiveness of risk management
Chapter 11 PSYCHOLOGY OF BEHAVIOR AND ASSESSMENT OF THE DECISION-MAKER
11.1. Personal factors affecting the degree of risk in making management decisions
11.1.1. Psychological problems of economic personality behavior
11.1.2. Management actions of an entrepreneur in the service sector
11.1.3. Personality Attitude to Risk
11.1.4. Intuition and risk
11.2. Expected Utility Theory
11.2.1. Utility Function Graphs
11.2.2. Expected Utility Theory
11.2.3. Taking into account the attitude of the decision maker towards risk
11.2.4. Group decision making
11.3. Rational behavior theory
11.3.1. Perspective theory
11.3.2. Rational decision making
11.3.3. Decision Asymmetry
11.3.4. Behavior invariance
11.3.5. The role of information in decision making
11.4. Conflict situations
11.5. The role of the leader in making risk decisions
11.5.1. Decision making at risk
11.5.2. Decision maker requirements
11.5.3. Principles for evaluating the effectiveness of decisions made by decision makers
Questions to repeat
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Introduction
1.1 Introductory remarks
1.4.2 Risk Management System
Chapter 2. Modeling the process of managing operational risk of credit organizations
2.1 Mathematical statement of the problem
2.2 Modeling losses
2.3 Modeling of dependent structures of random variables. Digging Functions
2.4 Modeling the frequency of occurrence of losses
2.5 Stochastic Monte Carlo model of random approximation
2.6 the calculation of the amount of risk capital 66
Chapter 3. Implementation of the operational risk management system
3.1 Development and implementation of an operational risk management system
3.2 the calculation of the amount of risk capital
3.3 Evaluation of economic efficiency and sustainability of the model
Conclusion
List of references
Applications
Introduction
mathematical operational risk economic
Economic and mathematical modeling is now at a stage when a qualitative leap has ripened. A huge number of diverse models has accumulated around the world. Whatever area of \u200b\u200bthe economy we take, there is always a whole range of mathematical, computer, verbal - meaningful models, one way or another related to it. Hundreds of scientific journals monthly publish descriptions of new models, or modifications and development of old ones.
All of them, although they are called models of the economy, are in fact models of some one of its areas, they explain one thing. Each of them contributes to the knowledge system about economics. The peculiarity of the process of understanding, human cognition of complex phenomena consists in their simplification, reduction to a simple image. Therefore, since cognition is infinite, the creation of models, also, apparently, has no limit.
In the framework of mathematical economics, with the help of formal means, the study of complex economic mechanisms is already encountering significant difficulties. Models cease to be as beautiful and complete as in classical cases, although they consider the most common or most economically feasible combinations of simple mechanisms.
From a practical point of view, any, even a very large amount of information in itself has no value. Pure data is not the kind of knowledge that is called "power." Information becomes power when it allows us to foresee the future, i.e. answer the main question when choosing a solution: "What will happen if?" To answer this question, in addition to data, it is necessary to have a model of the real world.
Where do the models come from and why are they practically absent in banking management systems? In the banking business, the process of creating adequate models is complicated by two objectively existing factors. The first is that, from a management point of view, a bank is an extremely complex object, consisting of many different subsystems, between which there are a large number of heterogeneous connections. The bank’s activity consists of a number of business processes that substantially depend on many external factors: legislative, economic, social, political.
In cybernetics, objects such as a bank are called complex systems, and the methods for studying them are called systems analysis methods. The most significant results in this area are associated with the study of operations - an approach based on the use of quantitative mathematical methods to assess decisions. However, the use of quantitative methods is possible only when the researcher has adequate mathematical models that are absent in banking.
The second factor is manifested in the fact that in banking (especially in the conditions of transition to the market) it is impossible to conduct targeted experiments that precede the formation of a hypothesis and allow you to test it in practice. The accumulation of personal experience among analysts is hindered by a dynamic change in the situation typical of modern Russia.
Most of all, financial science is connected with the analysis of profitability of investment activity. In addition to measuring profitability, bank analysts also deal with the uncertainty of revenue generation; risk analysis is associated with this uncertainty. The lack of development of these issues in our practice explains the need to study foreign experience in the aspect of its application in Russia.
The totality of indicators, methods and calculation models used in assessing the profitability of a banking strategy is the subject of new, dynamically developing scientific areas - financial mathematics and financial analysis, formed at the junction of modern finance theory and a number of mathematical disciplines, such as: econometrics, probability theory , mathematical statistics, operations research, theory of random processes.
The main goal of banking is to maximize profits; a practically equal task is also to minimize banking risks. A decrease in the rate of profit from banking operations, a decrease in the client base and a decrease in turnovers in customer accounts lead to the fact that the ratio between the bank’s profit and its operating costs becomes extremely unfavorable. Thus, a situation is created when banks are forced to look for ways to reduce costs and minimize risks. And this, in turn, makes banks pay special attention to financial analysis and methods of managing their resources.
The ability to take reasonable risks is one of the elements of a culture of entrepreneurship in general, and banking in particular. In market conditions, each of its participants adopts certain rules of a business game and, to a certain extent, depends on the behavior of partners. One of these rules can be considered a willingness to take the risk and take into account the possibility of its implementation in their activities.
One of the main types of risks of credit organizations is operational risk due to the uncertainty of the state and functioning of their internal and external environment. Losses from the occurrence of operational risk events can lead to significant direct and indirect losses, ruin of companies and even loss of life. The high-profile bankruptcies of recent years, which were caused, inter alia, by errors in the organization of the operational risk management system, testify to the scale and insufficient elaboration of the issues of assessing, preventing and minimizing losses from the occurrence of events related to operational risk. The lack of representative statistical information, the heterogeneous and individual for each credit institution operational risk profile makes it impossible to use generally accepted methods and models for measuring and managing financial risks, used in risk management theory, to analyze and manage operational risk.
The need to reserve capital for operational risk (including operational risk in calculating the capital adequacy ratio H1) became a reality for Russian commercial banks in August 2010, as this reflects the development strategy of the banking sector and the CBR policy on introducing risk-based approaches to credit assessment organizations.
Thus, the tasks of constructing an effective system for measuring, predicting and minimizing the operational risk arising in the course of the activities of credit organizations determine the relevance of the study.
The aim of the study is to develop methods and models for the integrated management of operational risk of credit organizations. In accordance with the indicated goal, the following tasks were set and solved in the work:
1. To conduct a study of existing models and methods of analysis and management of financial risks in relation to the specifics of operational risk.
2. Develop a comprehensive classification of events and operational risk factors, taking into account the specifics of the activities of credit organizations.
3. To develop the mathematical tools necessary for the analysis, measurement and management of operational risk, including:
· To pose and implement the task of mathematical modeling of random processes of loss occurrence, taking into account the presence of the effect of correlations between them;
· To develop and programmatically implement a stochastic algorithm for modeling the total amount of losses with a given structure of dependencies and calculating the amount of risk capital to cover them (taking into account the presence of various insurance covers and risk measures).
4. To develop a software implementation for modeling the process of managing the operational risk of a credit institution, to assess the sensitivity of the implemented methods to various perturbations of input parameters.
5. Determine the economic efficiency of the implemented operational risk management model. To develop guidelines for the organization of the operational risk management process in credit organizations.
The object of the thesis research is the operational risks arising in the course of the current activities of credit organizations. The subject of the thesis research is economic and mathematical methods and models of the operational risk management process as an element of the risk management system of a credit organization.
The theoretical and methodological basis of the study was the work of domestic scientists in the field of insurance, financial and actuarial mathematics, game theory, probability theory and mathematical statistics, theory of extreme values, random processes, numerical methods, risk management.
The scientific novelty of the study is to develop an integrated approach to managing operational risk based on a synthesis of the following tasks of economic and mathematical modeling: analysis of the processes of occurrence of losses, estimation of the total amount of losses, calculation of the amount of risk capital to cover them. The subject of protection is the following provisions and results containing elements of scientific novelty:
1. The problem of mathematical modeling of random processes of occurrence of losses of credit organizations associated with operational risk has been posed and solved, which allows for a more accurate assessment of the value of operational risk, compared with existing calculation methods.
2. A probabilistic modeling of the aggregated amount of losses has been implemented taking into account the presence of correlations between them, which allows a more accurate assessment of the total amount of losses, and it is reasonable to reduce the estimated value of the required risk capital to cover them.
3. A software implementation of stochastic modeling of the amounts of random processes (losses) with a predetermined structure of dependencies and calculating the amount of capital to cover them, taking into account the presence of various insurance programs and risk measures, has been developed. The sensitivity of the developed methods to various perturbations of the input parameters is estimated.
4. The economic efficiency of the application of the developed integrated model of operational risk management in credit institutions has been proved in comparison with existing methods and models of analysis and management of operational risk (in terms of saving the amount of risk capital).
The first chapter discusses the features of simulation of banking processes, the model of the bank’s functioning, the concept of risk in banking, the classification of bank risks and the risk management system.
In the second chapter, the problem of mathematical modeling of the processes of the onset of losses of credit organizations associated with operational risk is posed and solved. Mathematical models have been implemented and: methods for estimating, measuring and predicting the aggregate amount of aggregated losses, calculating and coherently distributing the amount of risk capital, a mechanism has been proposed to supplement their own data by mapping information on losses of external organizations, the effect of the time structure of money and the presence of a significance threshold has been taken into account when modeling amount of losses. The third section of the chapter gives the main facts of the theory of copulas necessary for modeling dependent random processes, discusses correlation measures that are invariant to monotonic transformations. An algorithm for stochastic modeling of random processes with known distribution functions and a predetermined dependence structure using the Gaussian copula is implemented. Using the theory of copulas, an algorithm for generating dependent processes modeling the frequency of occurrence of losses is implemented. Section 2.5 describes the Monte Carlo stochastic model developed and implemented in the MATLAB package for estimating the probability distributions of the total losses of a credit institution for the general case, using Gaussian and Student t-copulas and fast Fourier transform. This model formed the basis of the AMA model, the implementation results of which are discussed in the third chapter. As an alternative to the proposed Basel II quantile function VaR for calculating the amount of capital to cover operational risk, section 2.6 proposes the use of coherent risk measures. The measure (Expected ShortFall - ES), which satisfies the subadditivity condition, allows one to obtain results that are more resistant to various extreme distributions of losses. The problem of coherent distribution of risk capital between areas of activity - and / or divisions of a credit organization has been posed and solved. The result obtained is that in terms of non-atomic game theory the principle of coherent distribution of risk capital can be uniquely determined through the Auman-Shapley vector, which always exists and belongs to the core of the game.
In the third chapter, the main stages are developed - the implementation and informational support of the credit institution’s integrated operational risk management system. The key points of creating internal regulatory acts and methodologies governing the operational risk management process that are subject to mandatory coverage in accordance with the requirements of the Central Bank of the Russian Federation and the recommendations of Basel II are presented. In addition to calculating the quantitative indicators of operational risk, it is recommended to monitor the qualitative indicators of operational risk, which maximally characterize the main areas of activity of a credit institution that are subject to operational risk. Section 3.1 has developed a comprehensive system of indicators (CIAR - key risk indicators) for medium-sized credit institutions.
As a demonstration of the developed quantitative methods for managing operational risk, the second part of the third chapter considers a simplified implementation of the AMA model using the example of calculating the CaR value for a medium-sized credit bank. The values \u200b\u200bof risk capital calculated on the basis of different approaches and for different risk measures and significance levels are compared. Section 3.3 analyzes the sensitivity of the implemented model for various perturbations of the input parameters. The estimated economic effect of the implementation of the developed models and methods for managing the operational risk of credit organizations compared with existing approaches has been evaluated.
In conclusion, the main results and conclusions of the study are formulated.
Chapter 1. Analysis of existing mathematical models of the bank
1.1 Introductory remarks
As mentioned above, the main purpose of banking is to maximize profits; a practically equal task is also to minimize banking risks. This means that the policy of a commercial bank should be based on a thorough assessment and imitation of various situations, analysis of many factors affecting the size of profit. These factors determine the level of banking risk; the bank's task is to minimize it.
Bank return \u003d Return on credit + Return on investment:
where is the specific gravity of the go and go type of resources
DB - bank profitability,
KR - credit resources,
Central Bank - investments in securities.
Investors acquire assets, such as stocks, bonds or real estate, in order to earn income either from selling them at a higher price, or in the form of dividends, interest on coupons or rental payments. Lenders lend money in the hope of earning income in the form of interest payments upon full repayment of the loan by the borrower. Thus, lenders and investors have a common goal - to receive income or interest as a result of investment or crediting activities.
A decrease in the rate of profit from banking operations, a decrease in the client base and a decrease in turnovers in customer accounts lead to the fact that the ratio between the bank’s profit and its operating costs becomes extremely unfavorable. Thus, a situation is created when banks are forced to look for ways to reduce costs and minimize risks. And this, in turn, makes Russian banks pay special attention to financial analysis and methods of managing their resources.
The most important rule on which decision-making strategies are based on risk in the business arena:
Risk and profitability change in one direction: the higher the profitability, the higher the risk of the transaction, as a rule.
If banks want to raise additional funds, they must demonstrate to their customers that they fully take into account the risk-income ratio.
It is this thesis that is currently used in a number of the largest foreign banks.
Under the conditions of a planned economy, the understanding of risk and uncertainty as integral components of socio-economic development, as the most important scientific categories requiring a comprehensive study, was excluded. The formation in Russia of market relations and the corresponding economic mechanisms led to the return of the concept of risk to the theory and practice of managing economic objects of all levels and forms of ownership.
Much attention is paid to modeling banking processes abroad. The idea of \u200b\u200bmanaging a bank portfolio or end-to-end balance management originates in the modern portfolio theory, developed in the mid-1950s. The first attempts to apply modern portfolio theory to banking were carried out in the form of linear and quadratic models of mathematical programming. Although these models were quite slim in the classical sense, they were too limited and complicated for practical use. Their main value lies in the ability to penetrate into complete balance management. It is useful as an aid to understanding how to manage your portfolio and risk.
Portfolio management concepts are illustrated using a linear programming model. Of course, in order to bring reality to a two-dimensional problem, it was necessary to seriously simplify the statement of the problem.
Imagine the bank balance in the following simplified form:
where the Central Bank - securities
KR - loans,
DV - demand deposits,
SD - time deposits,
K is capital. Egorova N.E., Smulov A.S. Enterprises and banks: interaction, economic analysis and modeling.-M .; Business, 2002. S.61.
The profit on securities and the profit on loans are denoted by P cb and P cr, respectively. The costs of attracting deposits and capital are assumed to be zero. Hence the income or profit of the bank Pr is given by the equation:
We also give a classification of analytical banking programs:
1. The level in the organizational structure of the bank: senior management, middle level, performers.
2. Type of the analyzed operation: credit operations, securities, foreign exchange operations, other operations.
3. Type of problem to be solved: monitoring, analysis, optimization, modeling, forecast, planning, control.
4. Time lag analysis: current moment, short-term estimates, medium-term estimates, long-term estimates.
1.2 Features of the simulation of banking processes
The need for simulation modeling is due, first of all, to the peculiarities of the Russian market. A distinctive feature of the Russian financial market is its “subjectivity”, extreme dependence on non-economic factors and, as a result, a high degree of uncertainty that makes it difficult to make sound financial decisions.
This uncertainty is created by:
1. instability of the external environment of Russian banks, lack of clearly established rules and procedures for organizing various sectors of the financial market (institutional aspect);
2. the lack of a sufficiently developed apparatus for predicting the macroeconomic situation in uncertain conditions and analysis of the multiplicity of factors (instrumental aspect);
3. the impossibility of accounting and formalizing all the relationships for building an economic and mathematical model that adequately reflects the structure of the financial market (cognitive aspect);
4. unavailability of reliable information - the lack of a single information space "bank - client - financial market - state" (information aspect);
5. inadequate reflection of the real financial condition of the bank in the financial statements (balance sheet, etc.) and, therefore, the lack of financial transparency in the bank (accounting aspect). The use of traditional means of supporting management decisions and forecasting in these conditions is difficult, and all the more valuable is the possibility of using the method of simulation modeling. Emelyanov A.A. Simulation in risk management. - St. Petersburg: St. Petersburg Academy of Engineering and Economics, 2000. P.132.
Many modern software products are designed specifically to predict the situation in the financial market. These include stock market technical analysis tools, expert systems, and statistical packages. These products are intended primarily for decision makers in the government debt market.
The practice of using forecasting tools by banks and investment companies in trading on the securities market shows that the forecast is far from always reliable even from the point of view of the trend. One reason for this is the limited period of statistical observations.
In turn, simulation is a tool with which you can cover all areas of the bank: credit and deposit, stock, work with foreign currency assets. A bank simulation model (IMB) does not predict market behavior. Its task is to take into account the maximum possible number of financial factors of the external environment (foreign exchange market, securities market, interbank loans, etc.) to support the adoption of financial decisions at the level of the head of the bank, the treasury, and the asset and liability management committee.
In this sense, IMB in its functions closely adjoins the developed automated banking systems (ABS) of the western development, which are used by large international trading banks.
Modeling processes in the bank allows you to simulate the registration of bank transactions and take into account the information that the transaction contains. The application of this construction ideology is fully justified not only from the point of view of simulating real financial flows in the bank, but also from the point of view of the practical applicability of the simulation results in the activities of the bank's financial manager.
Indeed, the balance sheet is a secondary result of decisions made. Both in practice and at IMB, the manager, making one or another decision on the transaction, assesses its risks and consequences for the bank not at once, but throughout the life of the transaction.
Simulation models are an integral part of modern banking management. Asset and liability management, planning of large-scale operations requires reliable analytical techniques.
Simulation modeling systems are widely used for analysis, forecasting and studying various processes in various fields of economics, industry, scientific research, both purely theoretical and practical.
The use of such systems is most effective and justified for long-range forecasting and in situations where a practical experiment is impossible or difficult. Simulation is an information technology that works with a simulation model and allows you to evaluate its parameters (therefore, efficiency) in an accelerated time scale.
Simulation model - software that allows you to simulate the activity of any complex object. Sometimes simulated objects can be so complex and have such a large number of parameters that creating a simulation model in a standard high-level programming language may take too much time to justify the results. Emelyanov A.A. Simulation in risk management. - SPB: St. Petersburg Academy of Engineering and Economics, 2000. P.24
There are many tasks and situations that require the use of simulation technology. These include modeling bank scenarios, “checking” certain decisions, analyzing alternative strategies, and much more. A qualified specialist is able to cite dozens of typical and particular tasks requiring analytical techniques. These include the classical tasks of banking planning, and tasks of "home" origin, for example, coordination of schedules of obligations and receipts. Simulation models allow you to make both approximate estimates and express audit of decisions made, as well as detailed numerical forecasts and calculations. A quick analysis of the situation based on a compact model of medium complexity is a valuable opportunity for any bank manager.
Simulation models allow linking the activities of all divisions of the bank into a single whole. On this basis, it becomes possible to effectively organize the entire system of operational and strategic planning of a commercial bank. Through the use of streaming approaches, information on the activities of the bank and its services takes on a concise and easy to read form. It lends itself to quantitative and qualitative (substantial) analysis. A simulation model based on one of the expert packages is a reliable reference point for the bank management. The stream “picture” of the bank’s activities greatly facilitates both operational management and long-term planning of the bank’s work.
Simulation models can be embedded in the basis of the expert complex of a commercial bank. In this case, a simulation model created on the basis of one of the expert packages is connected by data exchange channels with other specialized software packages and database spreadsheets. Such a complex can operate in real time. In its capabilities, it is approaching large, expensive bank management automation systems.
Optimization models, including multicriteria ones, have a common property - the goal is known, to achieve which one often has to deal with complex systems, where it is not so much about solving optimization problems, but about research and prediction of states depending on the chosen control strategies. And here we encounter difficulties in implementing the previous plan. They are as follows:
1. a complex system contains many links between elements;
2. the real system is influenced by random factors, the accounting of which is not possible analytically;
3. The possibility of comparing the original with the model exists only at the beginning, and after applying the mathematical apparatus, since intermediate results may not have analogues in a real system. Emelyanov A.A. Simulation in risk management. -SPB: St. Petersburg Academy of Engineering and Economics, 2000. P.58.
Due to various difficulties arising in the study of complex systems, practice required a more flexible method, and it appeared - Simulation modeling.
Usually, a simulation model refers to a set of computer programs that describes the functioning of individual blocks of systems and the rules of interaction between them. The use of random variables makes it necessary to repeatedly conduct experiments with a simulation system (on a computer) and subsequent statistical analysis of the results. A very common example of the use of simulation models is the solution of the problem of mass service using the Monte Carlo method.
Thus, working with a simulation system is an experiment carried out on a computer. What are the benefits?
1. greater proximity to the real system than mathematical models;
2. The block principle makes it possible to verify each block before it is included in the common system;
3. the use of dependencies of a more complex nature, not described by simple mathematical relationships.
The listed advantages determine the disadvantages:
1. build a simulation model longer, harder and more expensive;
2. to work with a simulation system, it is necessary to have a computer that is suitable for the class;
3. the interaction of the user and the simulation model (interface) should not be too complicated, convenient and well-known;
4. the construction of a simulation model requires a more in-depth study of the real process than mathematical modeling. Emelyanov A.A. Simulation in risk management. -SPB: St. Petersburg Academy of Engineering and Economics, 2000. P.79.
The question arises: can simulations replace optimization methods? No, but conveniently complements them. A simulation model is a program that implements a certain algorithm, for which the optimization problem is previously solved to optimize control.
So, neither a computer, nor a mathematical model, nor an algorithm for its study alone can solve a rather complicated problem. But together they represent the force that allows you to know the world around you, to control it in the interests of man.
Given the complex of tasks facing bank analysts, this system should provide:
1. calculation of indicators of current and future financial condition of the bank;
2. forecasting the status of individual financial transactions and the balance sheet of the bank as a whole;
3. assessment of the attractiveness of individual financial transactions;
4. synthesis (formation) of management decisions;
5. assessment of the effectiveness of the management decision;
6. assessment of the completeness and redundancy of sets of indicators of the financial condition of the bank.
Performing any of these functions requires modeling the financial activities of the bank.
1.3 the model of the bank
The set of methods used for the analysis and modeling of banking is extensive and diverse. Throughout the evolution of the mathematical theory of banks, methods of mathematical statistics, the theory of optimal control, the theory of random processes, the theory of games, the theory of the study of operations, etc. were used. It should be remembered that the bank is a complex object that requires an integrated approach. It will be extremely difficult to create an integrated bank model simultaneously covering liquidity management, forming an asset portfolio, developing a credit and deposit policy, etc. Therefore, we will describe the functioning of the bank in a rather aggregated manner.
Consider the work of the bank on a sufficiently large time interval.
Let the bank receive income in the form of payment for its services for the settlement of guarantee operations, brokerage services (or other income independent of the asset portfolio) - and income from securities acquired with free funds that comprise the aggregate portfolio of banking assets.
Revenues from acquired securities are made up of interest on securities - and payments of invested funds upon redemption or sale of securities -
(in case of stock
where is the interest rate on the purchased securities
average time to maturity of securities acquired by the bank. Kolemaev V.A. Mathematical Economics. - M.: UNITY, 1998. S. 68.
The bank also receives borrowed funds from the placement of its securities at a speed of W. We will assume that the securities issued by the bank are initially placed and repaid at par, and the interest income on them is determined based on the situation in the financial market at the time of issue .
First of all, the bank directs the income received to pay the costs of raising funds, which consist of interest payments on placed securities - and payments of the principal amounts of borrowed funds -
where is the interest rate on the placed securities
Average time to maturity of securities issued by the bank.
In addition, the bank bears expenses independent of the volume of its liabilities -, where:
Consumer price index,
To pay rent of premises, to pay for telecommunications expenses, as well as other expenses that are not dependent on the amount of borrowed funds (liabilities).
Then the bank pays the necessary taxes. The bank uses the remaining funds for investments in its own infrastructure (domestic investments) - and for dividend payments -.
The fact that the bank is obliged to pay certain expenses from its net profit can be taken into account by increasing the amount of expenses by dividing by (1-tax rate). There are also taxes levied on the amount of income, regardless of the costs incurred in obtaining this income, such as a tax on road users. Such taxes can be taken into account by multiplying the amount of income in advance by (1-tax rate). Similar methods can take into account other features determined by tax deductions, therefore we will not consider below the problems associated with taxation and tax benefits for some securities, such as government securities. Note that the costs are paid by the bank in a certain order. First of all, the bank is obliged to redeem the previously issued securities and pay interest on them, then it pays expenses that are not dependent on the volume of liabilities, taxes, and only then can pay dividends.
If the bank has free cash, then it directs them to purchase securities (external investments) at a rate of -. In case of lack of funds, the securities in the portfolio of the bank can be sold, then it has a negative sign. Artyukhov SV., Bazyukina O.A., Korolev V.Yu., Kudryavtsev A.A. Optimal pricing model based on risk processes with random premiums. // Systems and means of informatics. Special issue. - M .: IPIRAN, 2005. P.102
The amount of money, securities acquired by the bank and securities placed by the bank change over time as follows:
where is the expenditure of money on the purchase of securities (the receipt of money from their sale), and is the sufficiently small time constant characterizing the quality of the bank’s assets, in the sense of liquidity. If a bank places all its assets in any one segment of the financial market, then for it there is a value characterizing the degree of development of this segment. In the general case, it turns out as a weighted average in terms of assets from values \u200b\u200bcharacterizing the degree of development of each of the "segments of the financial market in which assets are placed. Since we do not consider the problem of generating assets in this paper, A is assumed to be a given value.
The maximum amount of funds that a bank can raise by placing its own securities is limited and depends mainly on the amount of the bank’s equity, the structure of its balance sheet, the quality of the bank’s investment portfolio and other less important indicators of its performance. We assume that
where is the reliability coefficient of the bank,
The amount of the bank’s own funds.
The placement by the bank of its own securities, to attract borrowed funds, also takes place at a certain limited speed, therefore
where is the time constant characterizing the degree of development of the market for other securities issued by the bank. It depends on how developed the infrastructure of the bank is, how large is the number of market participants with whom the bank cooperates.
We introduce a variable - the value of the portfolio of acquired securities. Then equations (1.4) - (1.6) take the form
We introduce dimensionless controls: through which the rate of spending money on the purchase of securities and the rate of receipt of money from the placement of bank securities are expressed as follows:
The value corresponds to the purchase / sale of securities of third-party issuers as quickly as the efficiency of the securities market allows. The value corresponds to the most rapid bank borrowing, and a complete refusal to raise funds.
The main feature of money - which makes them significantly different from securities purchased by the bank, even government ones - is the ability to use them to pay for the bank's current expenses. The flow of payments cannot be made if there is no sufficient supply of money, therefore, the speed of payments is limited and depends on the amount of money:
where is the characteristic time of receipt of money in the bank (making payments). Restrictions of this type are called liquidity restrictions.
Payments made by the bank must be divided into two groups:
Obligatory payments. These include payments for the repayment of securities issued by the bank - payment of interest on securities - expenses that do not depend on the volume of liabilities - In practice, the bank may delay obligatory payments, but this will lead to serious financial losses, and with a long delay to its recognition insolvent and eventually liquidated. We will assume that the delay in obligatory payments is completely eliminated, that is, the bank is required to constantly maintain liquidity.
Optional payments. Making these payments depends on the management and owners of the bank. These include domestic investment - and dividends - pS 2.
To preserve liquidity, it is necessary that:
for all (1.11)
Thus, we obtain the first phase constraint for our problem - condition (1.11).
Note that from this inequality, under the condition of non-negativity in particular, it follows that for all
Making optional payments is also limited in speed:
According to this inequality, one can introduce dimensionless control so that:
Since the bank’s preservation of its share in the financial services market depends on the volume of domestic investment, expenses can be attributed, in a sense, to mandatory ones, at least in most of the planning area. (After reaching the planning horizon T, the bank can be liquidated by its owners). Since dividend payments cannot be negative, we get one more phase restriction:
for all (1.13)
Thus, we have come to the conclusion that domestic investment is indeed mandatory in the sense of restriction (1.13).
We will assume that in the planning area the bank does not receive “excess revenues”, that is, large profits compared to equity, independent of the volume of assets. Consequently, the maximum amount of money that he can attract and receive in the form of profit is limited to a certain constant i.e. for all, this is the third phase constraint (1.14).
An estimate can be obtained on the basis of the maximum amount of borrowings of the ratio of interest rates on attracting and placing funds, the amount of income that does not depend on the amount of assets -.
Note that in most of the planning area it should be close to zero, since it is not profitable for the bank to keep cash that does not generate income, because in the financial market there are always absolutely reliable government securities that bring fixed positive income.
The absence of “excess returns” also means the limited rate of growth of the securities rate in the planning area:
We will describe the interests of the bank (its owners) by the desire to maximize the discounted utility of future dividend payments over a sufficiently long time interval. We assume that the utility received from the immediate payment appears to be several times greater than the utility of paying the same amount of funds, taking into account inflation, but after a while . The coefficient is called the coefficient of discounting the utility of dividend payments. Then the maximized functional is written in the following form:
where is the utility function of dividend payments.
When the role of the utility of consumption is played, it is usually required that it be continuous, monotonous, concave, and bounded above, and also imposed on the condition. The last condition guarantees the positivity of current consumption at every moment in time. Since dividends may not be paid, we will not require the condition to be satisfied, assuming that the utility function has a low aversion to zero consumption.
If the utility function has a constant relative aversion to risk according to Arrow-Pratt: then it can be shown that it can be written as:
To get rid of a high aversion to zero consumption, consider a slightly modified utility function
In this case, the relative aversion to risk will depend on the volume of consumption:. Based on (1.9) and (1.11) we obtain
Instead of function (1.13), we consider a straight line passing through the points
Since the function (1.17) will be negative for any amount of dividends, that is, it is bounded above by zero and is continuous and monotonic for any. Such a utility function has zero relative disgust for risk according to Arrow-Pratt, and by varying the parameter you can only change the nominal value of dividend payments. This fact underlines the differences in relation to risk between a private consumer and a commercial organization. On the one hand, the latter does not have an aversion to risk, since it can exist indefinitely, compared with a person’s life span, and is not prone to dangers like living things. On the other hand, a private consumer who has spent 2 * M rubles receives more satisfaction from the first M rubles spent than from the subsequent ones, which determines the concavity of the utility function of consumption for individuals. We will consider that the doubling of dividend payments leads to a doubling of their usefulness for recipients, of which there are a lot of people, including both individuals and legal entities. This determines the linearity of the dividend payout utility function. In the future, we will use the utility function (1.17).
Thus, we obtain the optimal control problem in continuous time
In addition, there is a boundary condition under which it means that the bank is obliged to pay off its debt by the end of the planning period.
Here are the phase variables, are the controls. Here - the predicted values \u200b\u200bof the corresponding variables - are considered given non-negative functions of time, - constants having the dimension of time.
Note that if at some point it vanishes, then according to equation (1.21), i.e. the solution at this point does not decrease. Accordingly, if at some point it reaches a value, then the solution does not increase. Thus, under the controls, from equation (1.21), conditions and continuity, we get that over the entire segment the volume at the face value of the placed securities of the bank is non-negative, i.e., does not exceed the permissible maximum -, for all (generally speaking )
Then, from the conditions and conditions of non-negativity of the given functions, as well as non-negativity, we get that for all. Assuming continuity, it can be shown using equation (1.20), as for all. Further we will assume that both are continuous and piecewise continuous on.
Since it also follows from equation (1.20) that. Using this inequality, it is easy to show the existence of such that, for all.
We will not, as previously assumed, consider how the portfolio of securities acquired by the bank is formed, depending on the reliability, profitability and liquidity of the latter, as well as on the preferences of the bank's management. All bank assets will be presented in aggregated form - one variable.
It can be seen from the foregoing that the bank’s credit and deposit policy, defined in the management model and is inextricably linked to the dividend payment policy set by the management, therefore, we will further study them together.
For the convenience of further study of the work, we write separately the notation:
The amount of free cash of the bank — cash in cash at the bank’s cash desk, or money held by correspondent. bank accounts in settlement centers of the Central Bank of the Russian Federation, as well as on the correspondent. accounts in other banks
Securities purchased at par
Volume of placed securities at par
Income independent of the volume of assets (commission for cash management services, warranty operations, brokerage services, etc.)
Horizon planning
Bank equity (capital)
Bank reliability coefficient
The speed at which the bank spends money on maintaining the management apparatus, paying rent, etc. or expenses independent of the volume of the bank's liabilities in prices at the initial time
The rate of reinvestment in the infrastructure of the bank (domestic investment) in prices at the initial time
The rate of dividend payments in prices at the initial time
Current market rate of securities acquired by the bank
Market value of the bank's securities portfolio
The time constant characterizing the degree of development of the financial market, taking into account the distribution of the bank's assets by its sectors
Time constant characterizing the degree of development of the securities market issued by the bank
Nominal growth index of a portfolio of securities acquired by a bank. For each security purchased, the nominal rate is reduced to the annual rate, taking into account reinvestment, then the average weighted rate for all securities in the bank's portfolio is calculated. The index is defined as ln (1 + “average weighted annual rate”)
Effective growth index of a portfolio of securities acquired by a bank
Growth Index of Total Debt on Placed Securities. For each placed security, the nominal rate is reduced to the annual rate, taking into account the refinancing of the debt due to new placements of securities, then the average weighted average rate for all placed securities is calculated. The index is defined as ln (1 + + “average weighted annual rate”)
Average maturity of securities acquired by a bank - average maturity of securities issued by a bank - consumer price index
Inflation index
Typical time for making payments (cash receipts)
The velocity of money in the banking system
The speed of spending money on the purchase of securities of third-party issuers, or the receipt of money from their sale
The rate of receipt of money from the placement of bank securities
Dividend payout utility discount factor
Arrow-Pratt relative risk aversion, parameter used to set the dividend payout utility function
M * - the maximum amount of money that may belong to the bank
Dividend payout utility function, continuous, monotonous
Bank Dividend Management
Managing the allocation of free cash
Management of raising funds in the bank.
1.4 the Concept of risk in banking
Risk is the possible danger of any adverse outcome.
In market conditions, each of its participants adopts certain rules of the game and to a certain extent depends on the behavior of partners. One of these rules can be considered a willingness to take the risk and take into account the possibility of its implementation in their activities.
Risk is understood to mean the probability, or rather, the threat of a bank losing part of its resources, revenue shortfalls or the appearance of additional costs as a result of certain financial transactions. Shchelov O. Operational risk management in a commercial bank. Bookkeeping and banks, 2006 - No. 6. S.112
In a crisis, the problem of professional banking risk management, operational accounting of risk factors are of paramount importance for financial market participants, and especially for commercial banks.
The leading principle in the work of commercial banks in the transition to market relations is the desire to obtain the greatest possible profit. The greater the risks, the higher the expected profitability of the operation. Risks are formed as a result of deviations of actual data from assessments of the current state and future development.
The modern banking market is unthinkable without risk. The risk is present in any operation, only it can be of different scales and in different ways "mitigated", compensated. It would be extremely naive to look for options for banking operations that would completely eliminate the risk and guarantee a certain financial result in advance.
1.4.1 Classification of banking risks
In the process of their activities, banks are faced with a combination of different types of risks, differing in their place and time of occurrence, external and internal factors affecting their level, and, therefore, on the methods of their analysis and methods for their description. Lobanov A.A., Chugunov A.V. Encyclopedia of financial risk management. - M., Alpina Business Books, 2005. P.89. All types of risks are interrelated and affect the activities of the bank.
Depending on the sphere of influence or the occurrence of banking risk, they are divided into external and internal.
External risks include those that are not related to the activities of a bank or a specific client, political, economic and others. These are losses resulting from the outbreak of war, revolution, nationalization, the ban on payments abroad, the consolidation of debts, the introduction of an embargo, the abolition of import licenses, the aggravation of the economic crisis in the country, and natural disasters. Internal risks, in turn, are divided into losses on the main and auxiliary activities of the bank. The former represent the most common group of risks: credit, interest, currency and market risks. The second includes losses on the formation of deposits, risks on new activities, risks of bank abuse.
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RISK THEORY AND MODELING OF RISK SITUATIONS
LECTURE 1
- The concept of risk. Risk classification criteria.
- Mathematical apparatus for modeling and researching risk situations.
- The basic concepts of game theory. Classification of games.
1. The concept of risk. Risk classification criteria.
UNDERSTANDING RISK
Any area of \u200b\u200bhuman activity, especially economics or business, is associated with decision-making in the face of incomplete information.
Sources of uncertainty can be very diverse: the instability of the economic and political situation, the uncertainty of the actions of business partners, random factors, that is, a large number of circumstances that cannot be taken into account (for example, weather conditions, uncertainty of demand for goods, not absolute reliability of production processes, inaccuracy of information, etc.). Economic decisions, taking into account the above and many other uncertain factors, are made within the framework of the so-called decision theory - an analytical approach to choosing the best action (alternative) or sequence of actions. Depending on the degree of certainty of the possible outcomes or consequences of various actions faced by the decision maker (DM), three types of models are considered in decision theory:
the choice of decisions in the conditions of certainty, if it is known with respect to each action that it invariably leads to some specific outcome;
choosing a solution at risk if each action leads to one of the many possible particular outcomes, with each outcome having a calculated or expertly estimated probability of occurrence. It is assumed that the decision makers know these probabilities or can be determined by expert judgment;
the choice of solutions in case of uncertainty, when one or another action or several actions result in many private outcomes, but their probabilities are completely unknown or do not make sense.
The difference between risk and uncertainty refers to the way information is specified and is determined by the presence (in case of risk) or absence (in case of uncertainty) of the probabilistic characteristics of uncontrolled variables. In the noted sense, these terms are used in the mathematical theory of operations research, where they distinguish decision-making tasks at risk and, accordingly, in conditions of uncertainty. If it is possible to qualitatively and quantitatively determine the degree of probability of a particular option, then this will be a risk situation.
A risk situation is a form of uncertainty when the occurrence of an event is likely and can be determined.
That is, in a risk situation, it is objectively possible to assess the likelihood of events arising as a result of joint activities of production partners, counter-actions of competitors or opponents, the influence of the natural environment on the development of the economy, the implementation of science, the transition to a new level of technology, etc.
For risk about the howling situation are characteristic:
-uncertainty (the random nature of the event, which determines which possible outcomes are realized in practice);
-availability of alternative solutions;
-known or possible to determine outcome probabilities and expected results;
-probability of loss;
-probability of additional profit.
In a market economy, risk is the key to entrepreneurship. The problem of risk and profit is one of the key in economic activity, in particular in the management of production and finance.
In this context, it is appropriate to recall that in V. Dahl’s explanatory dictionary, “risking” means “taking the guesswork, doing the wrong thing, venturing, venturing out, doing something without the right calculation, being random, acting boldly, enterprisingly, hoping for luck". “Risky" means "courage, courage, determination, enterprise, acting at random, randomness."
In the dictionary of the Russian language S.I. Ozhegova "risk" is defined as "danger, the possibility of danger" or as "acting at random in the hope of a happy outcome."
We note an interesting paradox. Expressions such as: “He who does not take risks, he does not win”, “Risk is a noble cause”, “There is no business without risk”, etc. The opinion that “without risk there are no serious undertakings” and “big risk - great benefit ”, etc. At the same time, the expressions“ risk step ”,“ risky measure ”contain a clear shade of disapproval. The recommendations and instructions “avoid risk” and “minimize risk” are very popular.
Thus, “risk” is defined, on the one hand, as “the danger of something,” on the other hand, as “an act of chance, requiring courage, decisiveness, enterprise, in the hope of a happy outcome.”
An entrepreneur who knows how to take risks on time is often rewarded. The risk in entrepreneurial activity is naturally associated with management, with all its functions - planning, organization, operational management, personnel use, economic control. Each of these functions is associated with a certain risk measure and requires the creation of an adaptive management system. That is, a special risk management is also necessary, which is based on the knowledge of the economic nature of risk, the development and implementation of a strategy for dealing with it in entrepreneurial activity. In the conditions of market relations, the problem of accounting and risk assessment assumes independent and applied value as an important component of management theory and practice. Most management decisions are made at risk.
Risk is an activity related to overcoming uncertainty in a situation of inevitable choice, during which it is possible to quantitatively and qualitatively assess the probability of achieving the intended result, failure and deviation from the goal.
A quantitative assessment of the degree of risk, as well as the possibility of constructing confidence intervals by a known probability, allow more reliable impact on the economic process in question in order to increase profits and reduce risk.
To understand the nature of entrepreneurial risk, the relationship between risk and profit is fundamental. The entrepreneur is willing to take risks in the face of uncertainty, because along with the risk of losses, there is the possibility of additional income. Although it is clear that the entrepreneur is not guaranteed to make a profit, the reward for the time, effort and ability spent by him can be both profit and loss.
You can choose a solution that contains less risk, but the profit will be less. And at the highest risk, profit is at its highest.
At risk, the entrepreneur gets a chance to get superprofits and at the same time gets the opportunity to be at a loss. The desire to make money contradicts the goal of security. Revenues higher than normal, average rates are achieved, as a rule, as a result of risky actions. In economic theory and practice, it is proved that a certain share of risk is a necessary condition for generating income.
Along with this, there is an inverse relationship between the level of risk and liquidity.
The higher the liquidity level (company assets, etc.), the lower the risk level.
High return on assets can be achieved by minimizing stocks, which is fraught with disruption of operational processes and means the risk of liquidity loss. And excessive thrifty inevitably threatens asset turnover and profitability.
RISK CLASSIFICATION CRITERIA
The qualification risk system includes groups, categories, types, subspecies and varieties of risks.
By the nature of the consequences, that is, depending on the possible outcome (risk aboutevent) risks can be divided into two large groups: net risks and speculative risks.
Ø Net risksmean the possibility of obtaining a negative or zero result. The peculiarity of pure risks (they are sometimes called statistical or simple) is that they almost always suffer losses for entrepreneurial activity. Their causes may be natural disasters, accidents, illness of company managers, etc.
Ø Speculative risks expressed in the possibility of obtaining both positive and negative results. The peculiarity of speculative risks, which are also called dynamic or commercial, is that they entail either losses or additional profit for the entrepreneur, which may be caused by changes in exchange rates, changes in market conditions, changes in investment conditions, etc.
According to the sphere of origin, based on the spheres of activity, the following types of risks: production risk, commercial risk, financial risk.
Production risk - this is the risk associated with the enterprise's failure to fulfill its plans and obligations for the production of products, goods and services, other types of production activities, as a result of exposure to both the external environment and internal factors.
Commercial risk - this is the risk of losses in the process of financial and economic activity. The reasons for commercial risk may be a decrease in sales volumes, an unexpected decrease in purchases, an increase in the purchase price of goods, an increase in distribution costs, loss of goods in the process of circulation, etc.
Financial risk - this is the risk associated with the inability of the company to fulfill its financial obligations. The reasons for financial risk may be a change in the purchasing power of money, non-payment, change in exchange rates, etc.
Depending on the main cause of the risks, they are divided into the following categories: natural risks, environmental risks, political risks, transport risks, commercial risks.
To natural risks the risks associated with the manifestation of the elemental forces of nature: earthquake, flood, hurricane, tsunami, fire, epidemic, etc.
Environmental risks - These are the risks associated with environmental pollution.
Environmental pollution is classified as follows: natural environmental pollution is caused by natural phenomena, usually disasters (floods, volcanic eruptions, mudflows); anthropogenic pollution occurs as a result of human activities.
Environmental risk may arise during the construction and operation of the facility and be an integral part of industrial risk.
Political risks - These are the risks associated with the political situation in the country and the activities of the state. Political risks arise in violation of the terms of the production and trading process, which are not directly dependent on the business entity.
Political risks include:
uthe impossibility of carrying out economic activities due to hostilities, revolution, aggravation of the domestic political situation in the country, nationalization, confiscation of goods and enterprises, the imposition of an embargo, due to the refusal of the new government to fulfill the obligations assumed by the predecessors, etc.
uintroduction of a deferment (moratorium) on external payments for a certain period due to the onset of emergency circumstances (strike, war, etc.);
uadverse change in tax legislation;
uprohibition or restriction of the conversion of the national currency into the payment currency.
Transport risks - these are the risks associated with the transport of goods by road: road, sea, river, rail, air transport, etc.
Business risks mean the uncertainty of the results from this commercial transaction.
Structurally commercial risks are divided into property, production, trading, financial.
è Property risks - these are the risks associated with the probability of loss of property of the entrepreneur due to theft, negligence, overstrain of technical and technological systems, etc.
Property risk is the probability that the enterprise will lose part of its property, damage it and not receive income in the process of carrying out production and financial activities.
The property risk group can be divided into the following subspecies:
The risk of property loss resulting from natural disasters (fires, floods, earthquakes, hurricanes, etc.);
The risk of property loss due to the actions of intruders (theft, sabotage);
The risk of loss of property as a result of industrial emergencies;
The risk of loss or damage to property during transportation;
The risk of property alienation due to the action of local authorities or other owners.
In addition, for a particular manufacturing company, the risk of losing any particular type of property, such as computer equipment or certain types of raw materials, materials and components, is likely.
These risks can be reduced by insurance of certain types of property, as well as by establishing firm liability of financially responsible persons at the enterprise, ensuring the organization of the company's territory, developing and implementing organizational, technical, economic and other measures to prevent risks or minimize them.
è Production risks - these are the risks associated with the loss from production shutdown due to the influence of various factors, and above all with the death or damage of fixed and circulating assets (equipment, raw materials, transport, etc.), as well as the risks associated with the introduction of new equipment into production and technology.
è Trading risks- risks associated with loss due to delayed payments, refusal to pay during the transportation of goods, non-delivery of goods, etc.
è Financial risk associated with the probability of loss of financial resources (i.e. cash).
Financial risks are divided into two kinds: risks associated with the purchasing power of money and risks associated with investing capital (investment risks).
The risks associated with the purchasing power of money include the following varieties of risks: inflation and deflation risks, currency risks, liquidity risks.
Inflation risk - this is the risk that with rising inflation, cash incomes depreciate in terms of real purchasing power faster than they grow. In such conditions, the entrepreneur suffers real losses.
Deflationary risk - this is the risk that with an increase in deflation, a fall in the price level, a deterioration in the economic conditions of entrepreneurship and a decrease in incomes.
Currency risks constitute a danger of currency losses associated with a change in the exchange rate of one foreign currency against another, when conducting foreign economic, credit and other foreign exchange transactions.
Liquidity risks - these are risks associated with the possibility of losses in the sale of securities or other goods due to a change in the assessment of their quality and use value.
Currency risk includes three types of risks: economic risk, transfer risk, transaction risk.
è Economic risk for an entrepreneurial firm is that the value of its assets and liabilities may change up or down (in national currency) due to future changes in the exchange rate. This also applies to investors whose foreign investments - stocks or debt instruments - generate income in foreign currency.
è Translation risk has an accounting nature and is associated with differences in accounting for the assets and liabilities of the company in foreign currency. In the event that a depreciation occurs
è foreign currency in which the assets of the company are expressed, the value of these assets is reduced. It should be borne in mind that the risk of transfer is an accounting effect, but little or no reflects the economic risk of the transaction.
è More important economic point of view is transaction risk, which considers the impact of changes in the exchange rate on the future flow of payments, and therefore on the future profitability of the entrepreneurial firm as a whole.
è Transaction risk- this is the probability of cash foreign exchange losses on specific transactions in foreign currency. Such a risk arises from the uncertainty of the value in the national currency of a foreign exchange transaction in the future. This type of risk exists both when concluding trade contracts and when obtaining or providing loans. It consists in the possibility of changing the value of receipts or payments when converted in national currency.
In addition, one should distinguish between currency risk for the importer and risk for the exporter.
Deal risk for exporter - This is a fall in the foreign exchange rate from the moment of receipt or confirmation of the order until receipt of payment and during negotiations.
Transaction risk for the importer - This is the increase in the exchange rate in the period between the date of order confirmation and the day of payment.
Thus, when concluding contracts, it is necessary to take into account possible changes in exchange rates.
Investment risks include the following subspecies of risk: risk of lost profits, risk of reduced profitability, risk of direct financial losses.
Risk of lost profits - this is the risk of indirect (collateral) financial loss (unearned profit) resulting from the failure of an action (for example, insurance, hedging, investing, etc.).
Profitability risk may arise as a result of a decrease in interest and dividends on portfolio investments, on deposits and loans. Profitability risk includes the following varieties: interest rate risks and credit risks.
Risks of direct financial losses include the following varieties: stock exchange risk, selective risk, bankruptcy risk, as well as credit risk.
uExchange risk-this is the risk of losses from exchange transactions.
uSelective risk - this is the risk of the wrong choice of types of capital investment, the type of securities to invest in comparison with other types of securities in the formation of the investment portfolio.
uBankruptcy risk it is a danger as a result of the wrong choice of capital investment, the complete loss by the entrepreneur of his own capital and his inability to pay off his obligations.
In terms of duration over time, entrepreneurial risks can be divided into short-term and permanent.
Short-term risks that threaten the entrepreneur for a certain period of time (for example, transport risk, when losses may arise during the carriage of goods, or the risk of default on a specific transaction).
To constant risks These include those that continuously threaten business in a given geographical area or in a particular sector of the economy (for example, the risk of default in a country with an imperfect legal system or the risk of destruction of buildings in an area with increased seismic hazard).
Since the main task of an entrepreneur is to take risks prudently, without crossing the line beyond which bankruptcy of a company is possible, it should be highlighted acceptable, critical and catastrophic risks.
Allowable Risk - This is a threat of a complete loss of profit from the implementation of a project or from entrepreneurial activity as a whole. In this case, losses are possible, but their size is less than the expected entrepreneurial
arrived. Thus, this type of entrepreneurial activity or a specific transaction, despite the likelihood of risk, retain their economic feasibility.
The next degree of risk, which is more dangerous than acceptable, is critical risk. Critical risk It is associated with the danger of losses in the amount of the costs incurred to carry out this type of business or a separate transaction.
Wherein critical risk of the first degree It is associated with the threat of obtaining zero income, but with the reimbursement of material costs incurred by the entrepreneur.
Critical risk of the second degree associated with the possibility of losses in the amount of full
costs resulting from the implementation of this entrepreneurial activity, that is, losses of the intended revenue are likely and the entrepreneur has to reimburse the costs at his own expense.
Catastrophic refers to risk , which is characterized by danger, the threat of loss in an amount equal to or exceeding the entire property condition
entrepreneur. As a rule, such a risk leads to the bankruptcy of the company, since in this case it is possible to lose not only all the funds invested by the entrepreneur in a certain type of activity or in a particular transaction, but also his property. This is typical for a situation where an entrepreneurial company received external loans at the expected profit. If this risk occurs, the entrepreneur has to return loans from personal funds.
2. Mathematical apparatus for modeling and researching risk situations.
The role of quantitative assessment of economic risk increases significantly when it is possible to choose the optimal solution from the totality of alternative solutions. The optimal solution provides the greatest probability of the best result at the lowest cost and loss in accordance with the tasks of minimizing and programming risk.
The application of economic and mathematical methods makes it possible to conduct a qualitative and quantitative analysis of economic phenomena, to quantify the value of risk and market uncertainty and to choose the most effective (optimal) solution.
Mathematical methods and models allow you to simulate various business situations and evaluate the consequences when choosing solutions, without costly experiments.
We will use the methods of mathematical game theory, probability theory, mathematical statistics, statistical decision theory, and mathematical programming as mathematical means of decision-making under conditions of uncertainty and risk.
Many financial transactions (venture capital investment, stock purchase, selling operations, credit operations, etc.) are associated with a rather significant risk. They require to assess the degree of risk and determine its magnitude.
Entrepreneur risk quantitatively characterized by a subjective assessment of the probable (i.e. expected) value of the maximum and minimum income (loss) from a given capital investment. Moreover, the larger the range between the minimum and maximum income (loss) with an equal probability of their receipt, the higher the degree of risk.
The degree of risk is the probability of the occurrence of a loss event, as well as the amount of possible damage from it.
The choice of an acceptable degree of risk depends on the preferences of the head of the enterprise. Conservative leaders are not prone to innovation; they usually try
get away from any risk. Flexible executives seek riskier decisions if risk is voluntary. In a difficult situation, such managers are focused on more risky decisions, if they are confident in the professionalism of the performers.
A manager’s willingness to take risks is usually formed under the influence of the results of the implementation of past similar decisions made in the face of uncertainty.
The losses incurred dictate the choice of a cautious policy, and success leads to risk.
Most people prefer less risky options. However, the attitude to risk largely depends on the amount of capital available to the entrepreneur. During the evaluation of alternative solutions, the manager has to predict the possible results, while the decision is made in the conditions of certainty, when the manager can accurately assess the results of each alternative solution.
Risky decisions are those that involve obtaining any result with some degree of probability. This occurs in conditions of uncertainty, when factors requiring analysis and accounting are very complex, but there is no reliable or sufficient information about them. Then it is impossible to be sure of achieving certain results. Uncertainty is also characteristic of many decisions made in rapidly changing circumstances. This situation is very familiar to Russian entrepreneurs. Determining the choice, the manager considers a new project.
in conjunction with other options and with already established types of activities of firms. In order to reduce risk, it is advisable to choose the production of such goods (services), the demand for which changes in opposite directions, that is, with an increase in demand for one product, demand for another decreases, and vice versa.
Unfortunately, not every risk can be reduced through diversification. The fact is that entrepreneurship is affected by various macroeconomic factors, such as the expectation of a rise or crisis, the movement of bank interest rates, etc. The manager cannot reduce the risk arising from these processes by diversifying production. Making management decisions at the enterprise
involves close linking of all types of risk. However, the manager’s most reliable forecasts may not come true due to unexpected and unforeseen circumstances that are independent of the company itself (economic conflicts, sudden changes in the tastes of customers, actions of competitors, strikes, unexpected government decisions).
Therefore, in case of adverse events, various possibilities are provided for reducing negative consequences due to reserve funds, production capacities, raw materials, and finished products; materially supported plans for reorienting activities are being developed.
It is possible to significantly reduce the risk due to skilled work on forecasting and internal planning, self-insurance and insurance, transferring part of the risk to other persons or organizations through hedging, futures transactions, and the repurchase of options.
To quantify the risk, it is necessary to know all the possible consequences of any particular action and the probability of the consequences themselves.
Probability means the possibility of obtaining a certain result. With regard to economic problems, methods of probability theory come down to determining the values \u200b\u200bof the probabilities of the occurrence of events and to choosing from the possible events the most preferable event based on the highest mathematical expectation.
Risk is an action in the hope of a happy outcome on the principle of “lucky - not lucky”. The entrepreneur is forced to take risks due to the uncertainty of the economic situation. The greater the uncertainty of the economic situation, the greater the degree of risk.
The uncertainty of the economic situation is due to the following factors: lack of complete information, randomness, opposition.
Lack of complete information about the economic situation and the prospects for its change makes the entrepreneur look for an opportunity to acquire the missing additional information, and in the absence of such an opportunity, start acting at random, based on his experience and intuition.
The uncertainty of the economic situation is largely determined by the factor of chance. Randomness- this is something that happens in similar conditions in different ways, and therefore it cannot be foreseen and predicted in advance. The mathematical apparatus for studying random variables is given by probability theory. Probability allows you to predict random events. It gives them quantitative and qualitative characteristics. At the same time, the level of uncertainty and the degree of risk are reduced.
The uncertainty of the economic situation is largely determined by the counteraction factor. To counteractions relate catastrophes, fires and other natural phenomena, wars, revolutions, strikes, various conflicts in labor collectives, competition, changes in demand, accidents, thefts, etc. The entrepreneur in the course of his actions must choose a strategy that will allow him to reduce the degree of opposition, and consequently, to reduce the degree of risk. The mathematical apparatus for choosing a strategy in conflict situations is given by game theory.
The degree of risk is measured by two criteria:
The average expected value
Vibration (variability) of the expected result.
RISK MEASURE
The most common view is that risk measure a certain commercial (financial) decision or operation should be considered the standard deviation (the positive square root of the variance) of the value of the indicator of the effectiveness of this decision or operation.
Indeed, since the risk is caused by the non-determinism of the outcome of the decision (operation), the smaller the dispersion (dispersion) of the result of the decision, the more it is predictable, i.e. less risk.
If the variation (dispersion) of the result is zero, the risk is completely absent. For example, in a stable economy, operations with government securities are considered risk-free.
Most often, an indicator of the effectiveness of a financial decision (operation) is profit.
Let us consider as an illustration the choice of one person from one of two options
risk investment.
Let there be two projects A and IN , in which the specified person can invest.
Project A at some point in the future provides a random amount of profit.
Suppose its average expected value, the mathematical expectation, is equal to t Awith
dispersion . For the project IN these numerical characteristics of profit as random
values \u200b\u200bare assumed to be equal respectivelym B and . Quadratic mean
deviations are equal respectivelyS a and S b.
The following cases are possible:
1) t A = m B, S a < S b, should choose a project A ;
2) t A > m B, S a < S b, should choose a project A ;
3) t A > m B, S a = S b, should choose a project A;
4) t A > m B, S A\u003e S B ;
5) t A < m B, S A< S B .
In the last two cases, the decision to choose a project A or IN depends on the attitude to the risk of the decision maker.
In particular, in case 4) the project A provides higher average profit,
however, it is more risky. The choice is determined by what additional
the average profit is compensated for the decision maker the specified increase in risk.
In case 5) for the project A the risk is less, but the expected profit is less.
The subjective attitude to risk is taken into account in the Neumann-Morgenstern theory.
Consider an example of choosing an investment option.
Example. Let there be two investment projects. The first with a probability of 0.6 provides a profit of 15 million rubles, but with a probability of 0.4, you can lose 5.5 million rubles. For the second project with a probability of 0.8, you can get a profit of 10 million rubles. and with a probability of 0.2 lose 6 million rubles. Which project to choose?
Decision.
Both projects have the same average profitability of 6.8 million rubles:
0,6*15 + +0,4(-5,5) = 0,8*10 + 0,2(-6) = 6,8.
However, the standard deviation of profit for the first project is 10.04 million rubles:
1/2 = 10,04;
and for the second - 6.4 million rubles:
1/2 = 6,4.
Therefore, the second draft is more preferable.
Although the standard deviation of the solution efficiency is often used
as a measure of risk, it does not accurately reflect reality. There may be situations in which options provide approximately the same average profit and have the same root mean square deviations of profit, but are not equally risky. Indeed, if by risk we mean the risk of ruin, then the magnitude of the risk should depend on the value of the initial capital of the decision-maker or the company that he represents. The Neumann-Morgenstern theory takes this circumstance into account.
3. BASIC CONCEPTS OF THEORY OF GAMES. GAME CLASSIFICATION
Game theory is the theory of mathematical models for making optimal decisions in the face of uncertainty, opposing interests of various parties, and conflict.
Mathematical game theory is an integral part of operations research.
The tasks of operations research can be classified according to the level of information about the situation available to the decision maker.
The simplest levels of information about a situation are deterministic (when the conditions under which decisions are made are completely known) and stochastic (when
many possible variants of conditions and their probability distribution are known).
In these cases, the task is reduced to finding the extremum of the function (or its mathematical expectation) under given restrictions. Methods for solving such problems are studied in mathematical programming courses or optimization methods.
Finally, the third level is indefinite when many
options, but without any information about their probabilities. This level of information about the situation is the most difficult. This complexity turns out to be fundamental, since the very principles of optimal behavior may not be clear.
Game theory is the theory of mathematical models of decision-making under conditions of uncertainty, when the decision-maker (the “player”) has information only about the set of possible situations in which he is actually in one, about the set of decisions (“strategies”) that he can accept, and about the quantitative measure of the “gain” that he could get by choosing this strategy in this situation.
Establishing the principles of optimal behavior in the face of uncertainty, proving the existence of solutions satisfying these principles, specifying algorithms for finding solutions, make up the content of game theory.
The uncertainty that we encounter in game theory can have a different origin. However, as a rule, it is a consequence of the conscious activity of another person (s) defending their interests. In this regard, the theory of games is often understood as the theory of mathematical models for making optimal decisions in a conflict.
Mathematical "game theory" is the theory of mathematical models for making optimal decisions in a conflict.
Thus, models of game theory can, in principle, meaningfully describe very diverse phenomena: economic, legal and class conflicts, human interaction with nature, the biological struggle for existence, etc.
All such models in game theory are called games.
Conflict situation - a situation in which two (or more) parties pursue different goals, and the results of any action by each of the parties depend on the actions of partners.
The game - a mathematical model of a conflict situation.
Win(payment) - the outcome of the conflict.
Zero sum game - a pair game in which the gain of one of the players is equal to the loss of the other.
In progress in game theory, the choice of one of the options provided for by the rules of the game is called.
Personal movecalled one of the players' conscious choice of one of the possible moves in this situation and its implementation.
Random movecalled a choice of a number of possibilities, carried out not by the decision of the player, but by some random selection mechanism.
Player strategy - a set of rules that determine the choice of his actions for each personal move, depending on the current situation.
Game theory goal - determination of the optimal strategy for each player.
The mathematical description of the game comes down to listing all the players acting in it, indicating for each player all his strategies, as well as the numerical gain that he will receive after the players choose their strategies. As a result, the game becomes a formal object that can be mathematically analyzed.
Games can be classified according to various criteria.
Firstly , non-cooperative gamesin which each coalition (many players acting together) consists of only one player. The so-called cooperative theory of non-cooperative games allows for temporary association of players in a coalition during the game, followed by sharing the winnings or making joint decisions.
Secondly, coalition gamesin which decision-makers are united in fixed coalitions according to the rules of the game. Members of the same coalition are free to exchange information and make fully agreed decisions.
By winning the game can be divided into antagonistic and games with nonzero sum.
By the nature of obtaining information - on the game in normal form (players receive all the information intended for them before the start of the game) and dynamic games (information is received by the players during the development of the game).
By the number of strategies - on end and endless games.
LITERATURE
Balabanov I.T. Risk management.- M.: Finance and statistics, 1996. - 192 p.: Ill.
[ 2 ] . Dubrov A.M., Lagosha B.A., Khrustalev E.Yu. Modeling of risk situations in economics and business. Tutorial. - M.: Finance and Statistics, 2000. - 176 p.: Ill.
Petrosyan L.A., Zenkevich N.A., Shevkoplyas E.V. Game theory. Textbook. - SPb .: BVH-Petersburg, 2012. -432 p .: ill.
Tepman L.N. Risks in the economy. Textbook for universities. - M.: UNITY-DANA, 2002. - 380 p.
Shapkin A.S., Shapkin V.A. Risk theory and modeling of risk situations. Textbook. M .: Publishing and trading corporation "Dashkov and K 0", 2005. - 880 p.
The book reveals the essence of risk management, its organization, strategy, techniques, methods of risk reduction, including insurance.
The training manual discusses approaches to accounting for uncertainty and risk factors in economic practice, as well as mathematical models used for these purposes. Situations arising under conditions of uncertainty and lack of information when making management decisions are analyzed. The content is illustrated by applied tasks with solutions.
The textbook is intended for both initial and in-depth study of game theory. A systematic study of mathematical models of decision-making by several parties in a conflict has been carried out. A consistent presentation of a unified theory of static and dynamic games is presented. All the main classes of games are considered: finite and endless antagonistic games, non-cooperative and cooperative games, multi-step and differential games. To consolidate the material, each chapter contains tasks and exercises of varying degrees of complexity.
The manual is intended for students, graduate students and teachers of economic universities and faculties, students of business schools, heads of enterprises and organizations.
The textbook outlines the essence of uncertainty and risk, classification and factors acting on them; methods of qualitative and quantitative assessment of economic and financial situations in conditions of uncertainty and risk are given.
CONTROL QUESTIONS.
1. What is risk?
2. How do the concepts of “risk” and “uncertainty” differ?
3. What is a “risk situation”?
4. The economic consequences of risk situations. Give examples.
5. Give a definition of economic risk. Give examples of economic risks.
4. Give examples of classifications of economic risks.
6. Describe the relationship between risk and profit of financial transactions.
7. Is the concept of economic risks connected exclusively with those
risks whose occurrence leads to monetary damage?
8. What is the degree of risk?
9. What are the main factors of economic uncertainty?
10. What is a risk measure? How is it measured? Give examples.
11. Formulate the basic concepts of game theory.
12. What is the sign of the classification of games. Give examples of games.
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