Comparing Entropies in Portfolio Diversification with Fuzzy Value at Risk and Higher-Order Moment

Abstract

Credibility fuzzy value at risk in portfolio models is a reasonable solution when investors may face ambiguity, lack of historical data, and when avoiding normally or symmetrically distributed assumptions is needed. Credibility fuzzy membership function because having a self-duality axiom is analogous to measurable function on a probability space for the random variable. The primary aim of this paper is to solve the portfolio problem by using the third and fourth credibility moments in multi-objective higher-order moment portfolio models with different entropies. Firstly, Minkowski, Shannon, Yager, Renyi, and Gini-Simpson entropies are presented as new objective functions to solve corner solutions of conventional fuzzy multi-objective weighted credibility higher-order moment portfolio selection models. Secondly, because of the non-linearity nature of multi-objective models, a genetic algorithm is used to solve the models. Finally, proposed models are tested–using the data of Tehran Stock Exchange–and then evaluated–applying adjusted Sharpe Ratio as a portfolio performance technique.