A Novel Game-Theoretical Approach for The Possibilistic Mean - Variance Model

Abstract

Possibility theory is a significant tool to deal with the imprecise probability and benefit from the expert knowledge. Thus, the possibilistic mean - variance (MV) model is a considerable alternative for the portfolio selection problem. In this study, we propose an extension of the possibilistic MV model to the multiple market strategies where we assume that the possibility distributions of asset returns are given with triangular fuzzy numbers. The proposed extension, which is related to the game theory is given with a linear optimization problem. Thus, it can be solved with the Simplex algorithm as in this study. After giving the theoretical points, we illustrate it by using a numerical example. To the best of our knowledge, this is the first paper bringing the game theory and the possibilistic MV model together.

Keywords

• Fuzzy Logic
• Game Theory
• Linear Optimization
• Portfolio Selection
• Possibility Theory

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