Fractional portfolio optimization based on different risk measures in fuzzy environment

Chenyang Hu; Yuelin Gao; Eryang Guo; Chenyang Hu; Yuelin Gao; Eryang Guo

doi:10.3934/math.2025384

AIMS Mathematics

2025, Volume 10, Issue 4: 8331-8363. doi: 10.3934/math.2025384

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Research article

Fractional portfolio optimization based on different risk measures in fuzzy environment

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, Ningxia, China
2.
The Collaborative Innovation Center for Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, Ningxia, China
3.
The Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Yinchuan 750021, Ningxia, China

Received: 11 December 2024 Revised: 27 March 2025 Accepted: 02 April 2025 Published: 11 April 2025
MSC : 90C11, 90C27, 90C59

This paper introduces the idea of fractional programming in a portfolio model and builds four fractional programming portfolio optimization models based on various risk measures in a fuzzy environment, with the aim of addressing the complexity of historical data of real securities markets and the fundamental form of existing portfolio models. The four models build on the mean–variance(MV) model by adding a number of useful limitations, such as restrictions on short selling, proportionate investment boundary restrictions, and portfolio cardinality constraints, to better suit the requirements of genuine currency-related stock markets. For the portfolio optimization problem, which is a 0-1 mixed-integer fractional programming problem, a dual-loop hybrid heuristic algorithm is proposed. This algorithm incorporates the constraints of the model into the algorithm, thereby avoiding the drawbacks of the penalty function method. The empirical analysis part uses historical data to simulate investments and compare portfolio strategies under various risk metrics in order to show how well the models perform. The numerical results of the four models are also compared, showing that the models are suitable for different investors and that they are consistent with actual stock market conditions.
- fuzzy environment,
- portfolio optimization,
- realistic constraints,
- fractional programming,
- hybrid heuristic algorithm
Citation: Chenyang Hu, Yuelin Gao, Eryang Guo. Fractional portfolio optimization based on different risk measures in fuzzy environment[J]. AIMS Mathematics, 2025, 10(4): 8331-8363. doi: 10.3934/math.2025384

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Abstract

This paper introduces the idea of fractional programming in a portfolio model and builds four fractional programming portfolio optimization models based on various risk measures in a fuzzy environment, with the aim of addressing the complexity of historical data of real securities markets and the fundamental form of existing portfolio models. The four models build on the mean–variance(MV) model by adding a number of useful limitations, such as restrictions on short selling, proportionate investment boundary restrictions, and portfolio cardinality constraints, to better suit the requirements of genuine currency-related stock markets. For the portfolio optimization problem, which is a 0-1 mixed-integer fractional programming problem, a dual-loop hybrid heuristic algorithm is proposed. This algorithm incorporates the constraints of the model into the algorithm, thereby avoiding the drawbacks of the penalty function method. The empirical analysis part uses historical data to simulate investments and compare portfolio strategies under various risk metrics in order to show how well the models perform. The numerical results of the four models are also compared, showing that the models are suitable for different investors and that they are consistent with actual stock market conditions.

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