Quasi-efficient frontier of minimum risk portfolio under hybrid uncertainty

Abstract

The article develops a method for constructing a quasi-efficient frontier of the minimal risk portfolio with forbidden short sales in conditions of hybrid uncertainty of the possibilistic-probabilistic type. For this purpose, a generalized model of a minimal risk portfolio is constructed. To assess the risk of an investment portfolio, the variance of the portfolio is used, defined in a clear form in accordance with Feng’s approach. The model of acceptable portfolios is considered in the context of possibility/necessity. When constructing its equivalent deterministic analogue, the principle of expected possibility is used. The obtained equivalent deterministic analogues of the generalized minimal risk portfolio model, both in the case of a measure of possibility and necessity, are quadratic programming problems. The obtained algorithms for processing possibilistic information are based on a shiftscale representation of a fuzzy random variable. The approach is demonstrated on a model example using real data of the Russian financial market.