Elliptic entropy of uncertain random variables with application to portfolio selection

Abstract

This paper investigates an elliptic entropy of uncertain random variables and its application in the area of portfolio selection. We first define the elliptic entropy to characterize the uncertainty of uncertain random variables and give some mathematical properties of the elliptic entropy. Then we derive a computational formula to calculate the elliptic entropy of function of uncertain random variables. Furthermore, we use the elliptic entropy to characterize the risk of investment and establish a mean-entropy portfolio selection model, in which the future security returns are described by uncertain random variables. Based on the chance theory, the equivalent form of the mean–entropy model is derived. To show the performance of the mean–entropy portfolio selection model, several numerical experiments are presented. We also numerically compare the mean–entropy model with the mean–variance model, the equi-weighted portfolio model, and the most diversified portfolio model by using three kinds of diversification indices. Numerical results show that the mean-entropy model outperforms the mean–variance model in selecting diversified portfolios no matter of using which diversification index.