Credibilistic variance and skewness of trapezoidal fuzzy variable and mean–variance–skewness model for portfolio selection

Abstract

The fuzzy set theory is widely used to describe the uncertainty of financial markets in modern portfolio selection problems. In this study, the credibility theory (a popular branch of the fuzzy set theory) is applied to extend Markowitz’s mean–variance portfolio selection model into mean–variance–skewness portfolio selection model. For this, the returns on risky stocks are regarded as trapezoidal fuzzy variables. The credibilistic skewness is obtained originally for trapezoidal fuzzy variable, and the incorporation of the credibilistic variance of trapezoidal fuzzy variable enables the estimation of risk on portfolio return. To solve the proposed multi-objective optimization problem, a polynomial goal programming approach is suggested in this study. In addition, a dominant numerical analysis of the proposed work and its comparison with existing works are presented.

Keywords

• Credibility measure
• Trapezoidal fuzzy variable
• Credibilistic variance
• Credibilistic skewness
• Fuzzy portfolio selection