Optimal Portfolio Selection Using Multi-Objective Fuzzy-Genetic Method

Abstract

The purpose of investors is to maximize the expected returnin an acceptable level of risk. A genetic algorithm (GA) based on multi-objective fuzzy approach is presented in this paper to solve the multi-objective problem of portfolio selection. The expected return maximization and the risk minimization are the objective functions of the proposed portfolio selection problem. Since GA does not require prespecified information of the problem, it has more flexibility rather than the other nonlinear methods. Furthermore, the GA is able to model the nonlinear manner of the objective functions of the problem. In the proposed fuzzy-genetic method the objective functions are transmitted to a fuzzy domain using a fuzzy membership function and after that the weighted sum method is employed to determine the total objective function. Besides, the Pareto front of the objectives of return and risk are obtained by varying the weighting coefficients and solving the new single-objective problems. To demonstrate the effectiveness of the proposed method, a case study including several active companies is studied.