A Class of Fuzzy Portfolio Optimization Problems: E-S Models

This paper adopts the spread of fuzzy variable as a new criteria in practical risk management problems, and develops a novel fuzzy expectation-spread (E-S) model for portfolio optimization problem. Since the spread is defined by Lebesgue-Stieltjes (L-S) integral, its computation for general fuzzy variables is a challenge issue for research, and usually depends on approximation scheme and soft computing. But for frequently used trapezoidal and triangular fuzzy variables, the spread can be represented as quadratic functions with respect to fuzzy parameters. These new representations facilitate us to turn the proposed E-S model into its equivalent parametric programming problem. As a consequence, given the fuzzy parameters, the E-S model becomes a quadratic programming problem that can be solved by general purpose software or conventional optimization algorithms. Finally, we demonstrate the developed modeling idea via two numerical examples.