Mean-AVaR-Skewness-Kurtosis Optimization Portfolio Selection Model in Uncertain Environments

Subject Areas : Financial Mathematics

Farahnaz Omidi ¹ , Leila Torkzadeh ² , Kazem Nouri ³

1 - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran.
2 - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran.
3 - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran.

Received: 2024-07-09 Accepted : 2024-09-24 Published : 2024-10-29

Keywords: Portfolio optimization, Uncertain variables, Skewness, Kurtosis, Average Value-at-Risk, Mean AVaR-skewness-kurtosis Model,

Abstract :

Several research investigations have indicated that asset returns exhibit notable skewness and kurtosis, which have a substantial impact on the utility function of investors. Additionally, it has been observed that Average Value-at-Risk (AVaR) provides a more accurate estimation of risk compared to variance. This study focuses on the computational challenge associated with portfolio optimization in an uncertain context, employing the Mean-AVaR-skewness-kurtosis paradigm.The uncertainty around the total return is con-sidered and analyzed in the context of the challenge of selecting an optimal portfolio. The concepts of Value-at-Risk (VaR), Average Value-at-Risk (AVaR), skewness, and kurtosis are initially introduced to describe uncertain variables. These concepts are then further explored to identify and analyse relevant aspects within specific distributions. The outcomes of this study will convert the existing models into deterministic forms and uncertain mean-AVaR-skewness-kurtosis optimization models for portfolio selection. These models are designed to cater to the demands of investors and mitigate their apprehensions.

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