The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions

Year 2024, Volume: 11 Issue: 2, 535 - 550, 30.06.2024

Furkan Göktaş

https://doi.org/10.30798/makuiibf.1389261

Cited By: 1

Abstract

The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.

Keywords

Convex Optimization, Fuzzy Set, Normal Distribution, Portfolio Selection, Possibility Theory, Triangular Fuzzy Number

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