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Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns

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  • Qin, Zhongfeng

Abstract

The determination of security returns will be associated with the validity of the corresponding portfolio selection models. The complexity of real financial market inevitably leads to diversity of types of security returns. For example, they are considered as random variables when available data are enough, or they are considered as uncertain variables when lack of data. This paper is devoted to solving such a hybrid portfolio selection problem in the simultaneous presence of random and uncertain returns. The variances of portfolio returns are first given and proved based on uncertainty theory. Then the corresponding mean-variance models are introduced and the analytical solutions are obtained in the case with no more than two newly listed securities. In the general case, the proposed models can be effectively solved by Matlab and a numerical experiment is illustrated.

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  • Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
    • Handle: RePEc:eee:ejores:v:245:y:2015:i:2:p:480-488
    DOI: 10.1016/j.ejor.2015.03.017
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    1. Huang, Xiaoxia & Ying, Haiyao, 2013. "Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations," Economic Modelling, Elsevier, vol. 30(C), pages 61-66.
    2. Li, Shengguo & Peng, Jin & Zhang, Bo, 2013. "The uncertain premium principle based on the distortion function," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 317-324.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    Cited by:

    1. Naomi Pandiangan & Sukono Sukono & Endang Soeryana Hasbullah, 2021. "Quadratic Investment Portfolio Based on Value-at-risk with Risk-Free Assets: For Stocks of the Mining and Energy Sector," International Journal of Energy Economics and Policy, Econjournals, vol. 11(4), pages 175-184.
    2. Wang, Dan & Qin, Zhongfeng & Kar, Samarjit, 2015. "A novel single-period inventory problem with uncertain random demand and its application," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 133-145.
    3. Xiaoxia Huang & Liying Song, 2018. "An emergency logistics distribution routing model for unexpected events," Annals of Operations Research, Springer, vol. 269(1), pages 223-239, October.
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    5. Guo, Sini & Yu, Lean & Li, Xiang & Kar, Samarjit, 2016. "Fuzzy multi-period portfolio selection with different investment horizons," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1026-1035.
    6. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    7. Li, Bo & Huang, Yayi, 2023. "Uncertain random portfolio selection with different mental accounts based on mixed data," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    8. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    9. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2018. "A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution," Risks, MDPI, vol. 6(1), pages 1-15, March.
    10. Liu, Weilong & Zhang, Yong & Liu, Kailong & Quinn, Barry & Yang, Xingyu & Peng, Qiao, 2023. "Evolutionary multi-objective optimisation for large-scale portfolio selection with both random and uncertain returns," QBS Working Paper Series 2023/02, Queen's University Belfast, Queen's Business School.
    11. Jin, Xiu & Chen, Na & Yuan, Ying, 2019. "Multi-period and tri-objective uncertain portfolio selection model: A behavioral approach," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 492-504.
    12. Li, Bo & Lu, Ziqiang, 2023. "Uncertain random enhanced index tracking for portfolio selection with parameter estimation and hypothesis test," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    13. Zhongfeng Qin & Qiqi Li, 2023. "An uncertain support vector machine with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 611-629, December.
    14. Xiaoxia Huang & Xuting Wang, 2019. "Portfolio Investment with Options Based on Uncertainty Theory," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 929-952, May.
    15. Li, Bo & Li, Xiangfa & Teo, Kok Lay & Zheng, Peiyao, 2022. "A new uncertain random portfolio optimization model for complex systems with downside risks and diversification," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    16. Mingxuan Zhao & Yuhan Liu & Dan A. Ralescu & Jian Zhou, 2018. "The covariance of uncertain variables: definition and calculation formulae," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 211-232, June.
    17. Lin Chen & Jin Peng & Bo Zhang & Isnaini Rosyida, 2017. "Diversified models for portfolio selection based on uncertain semivariance," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 637-648, February.
    18. Lifeng Wang & Jinwu Gao & Hamed Ahmadzade & Zezhou Zou, 2023. "Partial Gini Coefficient for Uncertain Random Variables with Application to Portfolio Selection," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    19. 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.
    20. Weiwei Guo & Wei-Guo Zhang & Zaiwu Gong, 2024. "Modeling of linear uncertain portfolio selection with uncertain constraint and risk index," Fuzzy Optimization and Decision Making, Springer, vol. 23(3), pages 469-496, September.
    21. Kiran Bisht & Arun Kumar, 2022. "Stock Portfolio Selection Hybridizing Fuzzy Base-Criterion Method and Evidence Theory in Triangular Fuzzy Environment," SN Operations Research Forum, Springer, vol. 3(4), pages 1-32, December.

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