Using fuzzy computing for making decisions on the formation of an investment portfolio

Abstract

The diversification of the investment portfolio may be regarded as one of the ways to manage investment risk. One of the solutions to this problem is the approach of Markowitz. However, it uses a number of assumptions which are poorly consistent with the realities of investment processes. Thus, the requirement of statistical homogeneity cannot be achieved in real conditions. The use of to the subjective probabilities almost does not improve the situation. It is assumed that there are some projects (investment projects, food programs, securities) from which an investment portfolio is to be formed and investments in these projects should be appropriately distributed. The information about the projects is vague and its possible refinement is associated with unacceptable time and material costs. Besides, the necessary level of certainty is not guaranteed. The resulting estimates are expert ones and they do not always have a quantitative representation, often being approximate. A mathematical substantiation, an algorithm and practical implementation of the solution to the problem are given, this problem being regarded as a fuzzy analogue of a statistical game. This problem is formulated in a fuzzy statement and several ways to solve it are presented. An algorithm and computational and analytical methods of making a rational decision on the formation of the investment portfolio have been described. These methods are free from defects of other known approaches, making it possible to take into account the multiplicity of identical estimates of yield components of the investment portfolio which ultimately enhances the validity of the distribution of investment resources. The presented approach has been successfully applied to practice in the assessment of the options and management and economic decision-making in the economic analysis and portfolio management in a number of commercial banks.