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Fuzzy portfolio optimization model under real constraints


  • Liu, Yong-Jun
  • Zhang, Wei-Guo


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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    References listed on IDEAS

    1. Giove, Silvio & Funari, Stefania & Nardelli, Carla, 2006. "An interval portfolio selection problem based on regret function," European Journal of Operational Research, Elsevier, vol. 170(1), pages 253-264, April.
    2. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    3. Gupta, Pankaj & Mittal, Garima & Mehlawat, Mukesh Kumar, 2013. "Expected value multiobjective portfolio rebalancing model with fuzzy parameters," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 190-203.
    4. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    5. Zhang, Wei-Guo & Liu, Yong-Jun & Xu, Wei-Jun, 2012. "A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 222(2), pages 341-349.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Zhang, Wei-Guo & Zhang, Xi-Li & Xu, Wei-Jun, 2010. "A risk tolerance model for portfolio adjusting problem with transaction costs based on possibilistic moments," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 493-499, June.
    8. Corazza, Marco & Favaretto, Daniela, 2007. "On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1947-1960, February.
    9. Grootveld, Henk & Hallerbach, Winfried, 1999. "Variance vs downside risk: Is there really that much difference?," European Journal of Operational Research, Elsevier, vol. 114(2), pages 304-319, April.
    10. Deng, Xiao-Tie & Li, Zhong-Fei & Wang, Shou-Yang, 2005. "A minimax portfolio selection strategy with equilibrium," European Journal of Operational Research, Elsevier, vol. 166(1), pages 278-292, October.
    11. Sadefo Kamdem, Jules & Tassak Deffo, Christian & Fono, Louis Aimé, 2012. "Moments and semi-moments for fuzzy portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 517-530.
    12. Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2007. "Randomly generating portfolio-selection covariance matrices with specified distributional characteristics," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1610-1625, March.
    13. Zhang, Wei-Guo & Zhang, Xili & Chen, Yunxia, 2011. "Portfolio adjusting optimization with added assets and transaction costs based on credibility measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 353-360.
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    Cited by:

    1. repec:spr:annopr:v:272:y:2019:i:1:d:10.1007_s10479-018-2876-1 is not listed on IDEAS
    2. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(1), pages 1-14, February.
    3. repec:wsi:ijitdm:v:17:y:2018:i:03:n:s0219622018500190 is not listed on IDEAS
    4. repec:kap:compec:v:53:y:2019:i:4:d:10.1007_s10614-018-9833-6 is not listed on IDEAS
    5. repec:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2411-9 is not listed on IDEAS
    6. 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.
    7. repec:wut:journl:v:1:y:2018:p:57-74:id:1346 is not listed on IDEAS
    8. repec:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-016-2365-3 is not listed on IDEAS

    More about this item


    Portfolio selection; Fuzzy number; Real constraints; Multi-objective optimization; Genetic algorithm;

    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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