A new fuzzy programming approach for multi-period portfolio optimization with return demand and risk control

This paper considers a multi-period portfolio selection problem imposed by return demand and risk control in a fuzzy investment environment, in which the returns of assets are characterized by fuzzy numbers. A fuzzy lower semi-deviation is originally defined as the risk control of portfolio. A proportion entropy constraint is added as the divergence measure of portfolio. Based on the theories of possibility and necessity measures, a new multi-period portfolio optimization model with return demand and risk control is proposed. And then, the proposed model is transformed into a crisp nonlinear programming problem by using fuzzy programming approach. Furthermore, an improved differential evolution algorithm is designed for obtaining the optimal strategy. Finally, a numerical example is given to illustrate the practicality and efficiency of the proposed model and the corresponding algorithm.