Portfolio selection problems with random fuzzy variable returns

In this paper, two portfolio selection problems including probabilistic future returns with ambiguous expected returns are proposed. Until now, many researchers have proposed models of portfolio selection problems, and there are some models considering both random conditions and ambiguous conditions, particularly using fuzzy random variables. However, the model including the random fuzzy variables has not been proposed yet. Therefore in this paper, we propose a random fuzzy portfolio selection problem. The formulated problem is transformed into a nonlinear programming problem. Finally, we construct a solution method to find a global optimal solution of the problem.