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Fuzzy portfolio optimization model under real constraints

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  • Liu, Yong-Jun
  • Zhang, Wei-Guo

Abstract

This paper discusses a multi-objective portfolio optimization problem for practical portfolio selection in fuzzy environment, in which the return rates and the turnover rates are characterized by fuzzy variables. Based on the possibility theory, fuzzy return and liquidity are quantified by possibilistic mean, and market risk and liquidity risk are measured by lower possibilistic semivariance. Then, two possibilistic mean–semivariance models with real constraints are proposed. To solve the proposed models, a fuzzy multi-objective programming technique is utilized to transform them into corresponding single-objective models and then a genetic algorithm is designed for solution. Finally, a numerical example is given to illustrate the application of our models. Comparative results show that the designed algorithm is effective for solving the proposed models.

Suggested Citation

  • Liu, Yong-Jun & Zhang, Wei-Guo, 2013. "Fuzzy portfolio optimization model under real constraints," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 704-711.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:704-711
    DOI: 10.1016/j.insmatheco.2013.09.005
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    Cited by:

    1. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," JRFM, MDPI, vol. 10(1), pages 1-14, February.
    2. Yong-Jun Liu & Wei-Guo Zhang, 2018. "Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 941-968, May.
    3. Marco Corazza & Carla Nardelli, 2019. "Possibilistic mean–variance portfolios versus probabilistic ones: the winner is..," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 51-75, June.
    4. Liu, Yong-Jun & Zhang, Wei-Guo, 2015. "A multi-period fuzzy portfolio optimization model with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 242(3), pages 933-941.
    5. Chun-Hao Chen & Yu-Hsuan Chen & Vicente Garcia Diaz & Jerry Chun-Wei Lin, 2023. "An intelligent trading mechanism based on the group trading strategy portfolio to reduce massive loss by the grouping genetic algorithm," Electronic Commerce Research, Springer, vol. 23(1), pages 3-42, March.
    6. Vasileios E. Kontosakos, 2020. "Fast Quadratic Programming for Mean-Variance Portfolio Optimisation," SN Operations Research Forum, Springer, vol. 1(3), pages 1-15, September.
    7. Wei Chen & Yun Wang & Mukesh Kumar Mehlawat, 2018. "A hybrid FA–SA algorithm for fuzzy portfolio selection with transaction costs," Annals of Operations Research, Springer, vol. 269(1), pages 129-147, October.
    8. Chun-Hao Chen & Jonathan Coupe & Tzung-Pei Hong, 2023. "An Accelerated Optimization Approach for Finding Diversified Industrial Group Stock Portfolios with Natural Group Detection," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    9. K. Liagkouras & K. Metaxiotis, 2019. "Improving the performance of evolutionary algorithms: a new approach utilizing information from the evolutionary process and its application to the fuzzy portfolio optimization problem," Annals of Operations Research, Springer, vol. 272(1), pages 119-137, January.
    10. Anna Łyczkowska-Hanćkowiak, 2019. "Sharpe’s Ratio for Oriented Fuzzy Discount Factor," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    11. Adam Borovička, 2022. "Stock portfolio selection under unstable uncertainty via fuzzy mean-semivariance model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 595-616, June.
    12. Yong-Jun Liu & Wei-Guo Zhang, 2019. "Possibilistic Moment Models for Multi-period Portfolio Selection with Fuzzy Returns," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1657-1686, April.
    13. Wei Chen & Yuxi Gai & Pankaj Gupta, 2018. "Efficiency evaluation of fuzzy portfolio in different risk measures via DEA," Annals of Operations Research, Springer, vol. 269(1), pages 103-127, October.
    14. Krzysztof Piasecki & Joanna Siwek, 2018. "The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 57-74.
    15. Ruey-Chyn Tsaur & Chien-Liang Chiu & Yin-Yin Huang, 2021. "Fuzzy Portfolio Selection in COVID-19 Spreading Period Using Fuzzy Goal Programming Model," Mathematics, MDPI, vol. 9(8), pages 1-15, April.

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    More about this item

    Keywords

    Portfolio selection; Fuzzy number; Real constraints; Multi-objective optimization; Genetic algorithm;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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