Title: Fuzzy expectation-spread-skewness model for Shariah-compliant portfolio optimisation

Authors: Imen Ben Abdelwahed; Faouzi Trabelsi

Addresses: Department of Mathematics, Institut Supérieur d'Informatique et de Mathématiques de Monastir, Avenue de la Korniche, B.P. 223, 5000 Monastir, Tunisia; Faculté des Sciences de Monastir, Avenue de l'Environnement – Monastir – 5000, Tunisia; Laboratoire de Recherche 'Analyse, Probabilités et Fractals' (LR18ES17), Université de Monastir, Tunisia ' Department of Mathematics, Institut Supérieur d'Informatique et de Mathématiques de Monastir, Avenue de la Korniche, B.P. 223, 5000 Monastir, Tunisia; Faculté des Sciences de Monastir, Avenue de l'Environnement – Monastir – 5000, Tunisia; Laboratoire de Recherche 'Analyse, Probabilités et Fractals' (LR18ES17), Université de Monastir, Tunisia

Abstract: It is well known that fuzzy portfolios are very useful for investors who are looking for a path to manage risk when dealing with their long-term investment portfolio. In this paper, we propose a new framework to portfolio selection problem based on fuzzy theory in the context of Islamic finance. In order to measure how much an investor satisfies with his profit, skewness is adopted in addition to the first two moments of the distribution. We formulate a new fuzzy (Shariah-compliant) portfolio optimisation problem, referred as 'fuzzy expectation-spread-skewness (𝔽𝔼 - Sp - S) model'. We discuss the existence of the optimal solution. Besides, we provide numerical methods to approximate the solution, following in parallel probabilistic and analytical approaches. Some examples of application are also studied. Finally, we compare the followed numerical approaches and we state some financial interpretations.

Keywords: fuzzy portfolio; Shariah-compliant portfolio; fuzzy expectation; spread; skewness; triangular fuzzy variable; trapezoidal fuzzy variable; analytical approach; probabilistic approach.

DOI: 10.1504/IJOR.2021.117069

International Journal of Operational Research, 2021 Vol.41 No.4, pp.447 - 476

Received: 26 Mar 2018
Accepted: 02 Jan 2019

Published online: 16 Aug 2021 *

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