Formation of securities portfolio under conditions of uncertainty

Анотація

We examined a problem on the formation of securities portfolio. A criterion for portfolio effectiveness is determined – a probability that the total portfolio profitability exceeds a threshold. In connection with real shortage of the volume of initial data, we substantiated the rejection of hypothesis about the normality of their distribution law and the problem is solved under assumption about the worst distribution density of these data. In this case, it is accepted that mathematical expectation and the dispersion of values for the cost of assets are the fuzzy numbers. The form of membership function of the fuzzy parameters in the problem is selected. We constructed an analytical expression to describe the criterion in the terms of fuzzy mathematics.In this case, a problem on the maximization of fractional-quadratic functional with linear constraints is obtained. We devised a method for solving the obtained fuzzy problem of mathematical programming, which reduces this problem to the conventional problem of nonlinear programming. In order to solve this problem, it is proposed to employ the optimization method of zero order. It is demonstrated that the portfolio risk depends quadratically on the mathematical expectation of its profitability. Recommendations are given regarding the choice of numerical value for the mathematical expectation of portfolio profitability depending on the acceptable portfolio risk.

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