Portfolio Choice with Fuzzy and Fuzzy Random Returns

The aim of the paper is to propose and test the quality of the model for finding efficient portfolios using fuzzy-random asset returns in the form of a triangular number as well as fuzzy expectation, and a covariance matrix for returns in comparison with the basic formulation of the optimization problem of finding effective portfolios. In this paper, we carried out an empirical evaluation of effective portfolios on historical data and comparative analysis of their quality, and in conclusion considered the convergence of the 1st and 2nd moments for fuzzy random variables to their analogs for crisp numbers. It was found that the proposed modification of finding effective portfolios in terms of achieved returns and standard deviations does not show an unambiguous superiority over the model in the classical formulation, however, on the data not included in the training sample, the proposed model showed significantly better results compared with the model in the classical formulation.