Solving portfolio selection models with uncertain returns using an artificial neural network scheme

摘要

This paper presents a neural network model for solving two models for portfolio selection in which the securities are assumed to be uncertain variables. The main idea is to replace the portfolio selection models with linear programming (LP) problems. According to the convex optimization theory and some concepts of ordinary differential equations, a neural network model for solving LP problems is presented. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns. Two illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.