Portfolio optimization using elliptic entropy and semi-entropy of coherent fuzzy numbers

This paper explores the elliptic entropy and the elliptic semi-entropy of a coherent fuzzy number and discusses several of their properties. We propose a methodology that incorporates the adaptive index, k, of the coherent fuzzy number representing an individual investor’s stock market assessment (pessimistic, optimistic, or neutral). We combine the adaptive index with the elliptic entropy and semi-entropy to obtain risk measures incorporating investor attitude. We use the proposed risk measures in a portfolio optimization problem that uses coherent fuzzy numbers to model the asset returns. The optimization models are solved using a genetic algorithm. We apply the proposed methodology to a large-scale case study involving 100 assets to demonstrate its effectiveness. The real-world performance of the proposed approach is illustrated using an out-of-sample analysis. Based on the results we obtained, we discuss the advantages and disadvantages of elliptic entropy and semi-entropy. Finally, we compare the proposed methodology with other approaches in the literature and demonstrate its superiority.