Multi-objective Portfolio Selection Based on Skew-Normal Uncertainty Distribution and Asymmetric Entropy

Abstract

Empirical studies illustrate that in numerous cases the returns of securities are not normally distributed. In this paper, skew-normal uncertainty distribution is proposed to capture skewness in the portfolio selection problem. Furthermore, the concept of asymmetric entropy for uncertain variables as the quantifier of diversification is presented and its mathematical properties such as translation invariance and positive linearity are studied. To examine the effect of asymmetric entropy parameter on portfolio diversification, a mean-CVaR-entropy portfolio selection problem is presented based on asymmetric entropy with different parameter values and logarithm entropy. A non-dominated sorting genetic algorithm II (NSGA-II) is implemented in MATLAB to solve the corresponding problem. Numerical results show that asymmetric entropy for a specific parameter value will outperform logarithm entropy in portfolio diversification.