An Analysis of Alternative Methods of Measuring Economic Risk Within the Fuzzy Set Approach

The article is devoted to the problems of measuring economic risk on the basis of fuzzy sets. An analysis and further development of the methodical apparatus for quantitative assessment of the degree of economic risk is carried out within the framework of the interpretation of the degree of risk as the degree of possibility of discrepancy between the value of the criterion indicator and its normative level. As a direct subject of consideration, the case is taken when there is a simultaneous fuzziness of assessments of the criterion and the normative. The principal emphasis in the study is made on the computational aspect (computational versions) of the analyzed methods for assessing the degree of economic risk. Initially, one of the existing methods for measuring economic risk is considered, the scope of which is the situation when fuzzy assessments of the criterion economic indicator and its normative imply a horizontal, i.e. by levels of affiliation (alpha-levels) way of presentation. Based on the results of the analysis of expressions that define this method, its modification is proposed, which is based on the alpha-level weighing of its basic structural components. Comprehensive attention in the study is paid to the method of assessing the degree of risk for a fuzzy assessment of a criterion economic indicator in relation to a fuzzy assessment of the normative, which is based on a probabilistic analogy. Within this framework, the formulas that form the computing apparatus of this methodical approach are systematized and supplemented. Among other things, the generalized computational formulas of the commented method have been supplemented. For the conditional situation, on the basis of a series of simulation computations, a comparative analysis of the studied alternative methods of measuring economic risk is carried out. The accomplished analysis made it possible to identify certain regularities of the mutual distribution of values of the degree of risk, obtained when they are applied simultaneously

Estimation of Input Financial and Economic Parameters of an Investment Project Based on a Fuzzy Set Approach

The article considers the problem of estimating input financial and economic parameters of investment projects in the form of fuzzy quantities (numbers). The results of the study give grounds to state that the modern fuzzy set methodology comprises a sufficiently developed arsenal of methods for constructing the membership functions of fuzzy sets, some of which can be used for carrying out economic analysis and evaluating real investment. At the same time, the issue of estimating input financial and economic parameters of investment projects has its own peculiarities, thus when addressing it, the turning to general approaches should be complemented with elaborating and developing special methods. Such special methods, in particular, are the method based on quasi-statistics and the method of reference points. The paper proposes an approach to finding fuzzy estimates of the input financial and economic parameters of real investments, which, in accordance with its logic, was called the method of reference intervals. The constructive principle of this method is to represent a sought-for fuzzy estimate using the interval approximations of its core and carrier. The specified interval approximations, which are interpreted as reference intervals, are determined on the basis of the principles of the theory of rough sets. A promising direction of further scientific research on the issues touched upon in the publication is the development of a methodological apparatus for considering the combined uncertainty in the structure of input data when modeling economic efficiency of real investment

Analytical Support for Selecting the Best Investment Project in the Presence of Fuzzy Data

The article is dedicated to the problem of optimal choice in the field of real investments in case of fuzzy estimates of financial and economic parameters. The general methodological basis of the research is an integrated approach to solving decision-making problems under conditions of uncertainty, conflict, and risk generated by them, based on the game theory, proposed by R. I. Trukhayev. In recent decades, it has been actively developed in papers by the followers of the scientific school of riskology under the leadership of V. V. Vitlinsky. One of the system-forming components of the above integration and game methodology is the classifier of information situations (there singled out seven of them). In this case, the description of possible states of the economic environment by a fuzzy set (a subset) corresponds to the seventh information situation. An attempt was made to develop a methodical apparatus for the task of selecting the best investment project from a variety of alternative projects in the presence of fuzzy data. As a result, a model based on the use of convolutions of local criteria is formulated. In accordance with the accepted methodological guidelines, the structure of the generalized (integral) indicator of the economic attractiveness (efficiency) of real investment provides for three hierarchical levels: 1) the level of detailed criteria in terms of partial criteria (financial effect, profitability, payback period), 2) the level of partial criteria, 3) the level presenting the very generalized indicator. In the basic version of the proposed model, among the possible techniques (methods) for aggregating indicators detailing the aspects of fuzzy estimates of partial criteria, the preference is given to the method by which they are joined by a combined, additive and multiplicative convolution

Estimation of the Net Present Value of the Investment Project in the Situation of Fuzzy Initial Data

The article investigates the problem of estimating the net present value of the investment project using a methodology based on the theory of fuzzy sets in the situation when the initial data are described by fuzzy estimates. In the general case the fuzzy-multiple estimation of the specified indicator at a discrete-interval representation of the initial parameters is reduced to a set of homogeneous optimization problems. Often, depending on the characteristics of fuzzy estimates of cash flows of the investment project under consideration, the solutions to these problems can be found directly on the basis of relevant analytical expressions, while other problems require using special optimization methods. In the work there made an attempt to develop the analytical component of the fuzzy-multiple modeling of the net present value indicator. First, we examined the general search and optimization approach, which allows providing a predetermined degree of accuracy, as well as the method for approximate determination of the fuzzy estimate of the net present value on the basis of analytical relationships developed by Сhui-Yu Chiu and Chan S. Park. After that, the situation was analyzed, and the corresponding calculation model was proposed, when fuzzy estimates of the cash flows of the investment project can be interpreted from the perspective of the concept of the money-generating operation formulated by O. B. Lozhkin. Among other things, it allowed to develop a general scheme for determining the fuzzy estimate of the net present value, supplementing it with the situation of this concept. As the main direction of the further development of the problems discussed in the publication there determined the formation of a holistic methodology for evaluating the effectiveness of real investments, which would cover different in their nature and structural characteristics types of uncertainty from unified theoretical positions

Optimizing an Investment Solution in Conditions of Uncertainty and Risk as a Multicriterial Task

The article is concerned with the methodology for optimizing investment decisions in conditions of uncertainty and risk. The subject area of the study relates, first of all, to real investment. The problem of modeling an optimal investment solution is considered to be a multicriterial task. Also, the constructive part of the publication is based on the position that the multicriteriality of objectives of investment projecting is the result, first, of the complex nature of the category of economic attractiveness (efficiency) of real investment, and secondly, of the need to take into account the risk factor, which is a vector measure, in the preparation of an investment solution. An attempt has been made to develop an instrumentarium to optimize investment decisions in a situation of uncertainty and the risk it engenders, based on the use of roll-up of the local criteria. As a result of its implementation, a model has been proposed, which has the advantage that it takes into account, to a greater extent than is the case for standardized roll-up options, the contensive and formal features of the local (detailed) criteria

Rational Choice of the Investment Project Using Interval Estimates of the Initial Parameters

The article is dedicated to the development of instruments to support decision-making on the problem of choosing the best investment project in a situation when initial quantitative parameters of the considered investment alternatives are described by interval estimates. In terms of managing the risk caused by interval uncertainty of the initial data, the study is limited to the component (aspect) of risk measure as a degree of possibility of discrepancy between the resulting economic indicator (criterion) and its normative level (the norm). An important hypothesis used as a basis for the proposed in the work formalization of the problem under consideration is the presence – for some or all of the projects from which the choice is made – of risk of poor rate of return in terms of net present (current) value. Based upon relevant developments within the framework of the fuzzy-set methodology and interval analysis, there formulated a model for choosing an optimal investment project from the set of alternative options for the interval formulation of the problem. In this case it is assumed that indicators of economic attractiveness (performance) of the compared directions of real investment are described either by interval estimates or possibility distribution functions. With the help of the estimated conditional example there implemented an approbation of the proposed model, which demonstrated its practical viability

Estimating the Economic Attractiveness of Investment Projects in Conditions of Uncertainty and Risk with the Use of Sensitivity Analysis

The article is concerned with the methodology of economic substantiation of real investments in case of considerable lack of information on possible fluctuations of initial parameters and the resulting risk. The analysis of sensitivity as the main instrument for accounting the risk in the indicated problem situation is the focus of the presented research. In the publication, on the basis of the apparatus of interval mathematics, a set of models for comparative estimation of economic attractiveness (efficiency) of alternative investment projects in conditions of uncertainty and risk is formulated, using the sensitivity analysis. The developed instrumentarium assumes both mono- and poly-interval version of the sensitivity analysis. As the risk component in the constructed models is used: in some – values of the specially developed sensitivity coefficient, in others – the worst values, which are based on the interval estimations of the partial criteria of efficiency. The sensitivity coefficient, according to the approach proposed in the publication, is the ratio of the target semi-range of variation to the increase (economy) of efficiency, which is provided when the basic level of the analyzed partial criterion of economic attractiveness in comparison with some of its threshold (limit) value is being reached

The Fuzzy Adaptation of Probabilistic Risk Indicators

The aim of the article is to develop fuzzy tools for measuring risk based on adaptation of corresponding indicators developed within the methodology of the probability theory. The study is limited to the situations where the economic indicator, which performs the function of a decision criterion and is an object of the analysis of the degree of risk, is modeled by a fuzzy number, and the latter is to be understood as a fuzzy value with a normal and convex membership function. Also in this case there applied the interval method, which describes fuzzy estimation of the criterion index by membership degrees. Within the framework of implementing the goal set, there consistently considered a number of probabilistic indicators of risk degree: mean absolute deviation, semideviation, coefficient of unfavorable deviations, ratio of expected losses (losses). For the latter, a modified version is proposed, in which the expected favorable and unfavorable deviations of the values of the criterion index are estimated taking into account the probability of their occurrence due to which it was called the weighted expected loss ratio. For the initial and modified version of the expected loss ratio, their fuzzy adaptations are formulated. According to the known property of the semideviation index, in the situation of probabilistic uncertainty the values of the coefficient of unfavorable deviations and the weighted expected loss ratio coincide. If the analyzed criterion index is described by a fuzzy estimate, the use of fuzzy adaptations of these coefficients in the general case leads to different results. It is also revealed that the fuzzy adaptation of the coefficient of unfavorable deviations coincides with the indicator of the degree of risk on the basis of a combined (hybrid) version of the possibility measure