Renyi entropy of uncertain random variables and its application to portfolio selection

This paper proposes a new type of entropy called Renyi entropy as an extension of logarithm entropy in an uncertain random environment and applies it to portfolio selection. We first define Renyi entropy and partial Renyi entropy to measure the indeterminacy of uncertain random variables and examine their mathematical properties. Then, we provide an approach for calculating partial Renyi entropy for uncertain random variables through Monte Carlo simulation. Next, we introduce Renyi cross-entropy and the concept of partial Renyi cross-entropy of uncertain random variables. As an application in finance, partial Renyi entropy is invoked to optimize portfolio selection of uncertain random returns. Numerical examples are displayed for illustration purposes. Finally, we compare the investment strategies adopted by the mean-Renyi entropy models with those of the mean-elliptic entropy models and the mean-variance models.