Portfolio Selection Problem in Fuzzy Random Decision Systems

Based on equilibrium chance theory, this paper presents a new class of fuzzy random minimum risk portfolio selection problem. In this problem, values of some functions are numerical characteristics of fuzzy random phenomena dependent on decision variables. This feature leads to the main difficulty encountered in solving the proposed portfolio selection problem. Therefore, conventional solution methods can not be applied to solving this problem. In order to solve the proposed portfolio selection problem, we use a sequence of finitely supported primitive fuzzy random variables to approximate a continuous fuzzy random vector, which result in a finite-dimensional fuzzy random minimum risk portfolio selection problem. We also discuss the convergence of the approximation method. After that, we integrate the approximation method and particle swarm optimization (PSO) algorithm to design a hybrid PSO algorithm to solve the proposed portfolio selection problem, and provide a numerical example with four assets to demonstrate the feasibility and effectiveness of the proposed algorithm.