Portfolio Optimization of Uncertain Returns Based on Tsallis Entropy

Abstract

In uncertainty theory, entropy is a measure to capture the level of unpredictability associated with an uncertain variable. In this paper, we introduce an alternative type of entropy named Tsallis entropy as a generalized form of logarithmic entropy in an uncertain environment. Then, we provide a formula to calculate the Tsallis entropy via inverse uncertainty distribution. In addition, we study some of its mathematical properties such as translation invariance and positive linearity. Furthermore, we establish a mean-CVaR-Tsallis entropy portfolio selection model, in which security returns are regarded as uncertain variables and we derive its equivalent form. Finally, a numerical example is given and the effect of Tsallis entropy and uncertainty distribution on the proposed model is discussed, including a comparative study.