An optimistic value–variance–entropy model of uncertain portfolio optimization problem under different risk preferences

Abstract

For the traditional portfolio optimization problems, the return rates of risky assets are described by random variables or fuzzy variables. Due to the complexity of real asset market, this assumption may not always be satisfactory, for example, when there are not enough available data. Hence, return rates can be treated as uncertain variables in many cases. In this paper, we consider an uncertain portfolio optimization problem under different risk preferences. First, an optimistic value–variance–entropy model is formulated, where optimistic value and entropy are used for measuring investment return and diversification, respectively. Then, a three-step method is proposed for solving the formulated model with considering different risk preferences. Finally, a comparison is presented in numerical simulation for illustrating the practicality and effectiveness of our models and solution method.