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A Novel Improved Genetic Algorithm for Multi-Period Fractional Programming Portfolio Optimization Model in Fuzzy Environment

Author

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  • Chenyang Hu

    (School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
    The Collaborative Innovation Center for Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China)

  • Yuelin Gao

    (School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
    The Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Yinchuan 750021, China)

  • Eryang Guo

    (School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
    The Collaborative Innovation Center for Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China)

Abstract

The complexity of historical data in financial markets and the uncertainty of the future, as well as the idea that investors always expect the least risk and the greatest return. This study presents a multi-period fractional portfolio model in a fuzzy environment, taking into account the limitations of asset quantity, asset position, transaction cost, and inter-period investment. This is a mixed integer programming NP-hard problem. To overcome the problem, an improved genetic algorithm (IGA) is presented. The IGA contribution mostly involves the following three points: (i) A cardinal constraint processing approach is presented for the cardinal constraint conditions in the model; (ii) Logistic chaotic mapping was implemented to boost the initial population diversity; (iii) An adaptive golden section variation probability formula is developed to strike the right balance between exploration and development. To test the model’s logic and the performance of the proposed algorithm, this study picks stock data from the Shanghai Stock Exchange 50 for simulated investing and examines portfolio strategies under various limitations. In addition, the numerical results of simulated investment are compared and analyzed, and the results show that the established models are in line with the actual market situation and the designed algorithm is effective, and the probability of obtaining the optimal value is more than 37.5% higher than other optimization algorithms.

Suggested Citation

  • Chenyang Hu & Yuelin Gao & Eryang Guo, 2024. "A Novel Improved Genetic Algorithm for Multi-Period Fractional Programming Portfolio Optimization Model in Fuzzy Environment," Mathematics, MDPI, vol. 12(11), pages 1-26, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1694-:d:1404853
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    References listed on IDEAS

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    1. Plachel, Lukas, 2019. "A unified model for regularized and robust portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
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