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Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns

Received: 30 June 2021     Accepted: 16 July 2021     Published: 23 August 2021
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Abstract

Diversification portfolio selection problem is an important issue in uncertain economic environment. In this paper, this problem is discussed within the framework of uncertainty theory. First, an uncertain extension mean-variance diversification model is proposed, in which the mean is chosen as the objective function, and variance and proportion entropy as risk and diversity constraints. Then two variations are investigated on the purposes of minimizing the risk and maximizing the diversity measure, respectively. Furthermore, the corresponding analytical mathematical models are deduced via the convenient operational law of uncertain variables. Finally, several numerical examples are given to illustrate the modeling idea. The results showed that the diversification models had higher diversification than the uncertain mean-variance model. The proposed models provide a new method to make decision-making in uncertain portfolio selection problem.

Published in International Journal of Management and Fuzzy Systems (Volume 7, Issue 3)
DOI 10.11648/j.ijmfs.20210703.12
Page(s) 47-54
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Portfolio Selection, Uncertain Variable, Entropy, Uncertainty Modeling

References
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[5] B. Zhang, J. Peng, S. Li, Uncertain programming models for portfolio selection with uncertain returns, InternationalJournalofSystemsScience46(2015)2510– 2519.
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[9] I. Usta, Y. Kantar, Mean variance skewness entropy measures: a multi-objective approach for portfolio selection, Entropy 13 (2011) 117–133.
[10] J. Chang, L. Sun, B. Zhang, J. Peng, Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory, Journal of Computational and Applied Mathematics 377 (2020) 112892.
[11] J. Kapur, H. Kesavan, Entropy Optimization Principles with Applications, Academic Press, New York, 1992.
[12] K. Yao, A formula to calculate the variance of uncertain variable, Soft Computing 19 (2015) 2947–2953.
[13] L. Chen, J. Peng, B. Zhang, I. Rosyida, Diversified models for portfolio selection based on uncertain semivariance, International Journal of Systems Science 48 (2017) 637–648.
[14] L. Yan, Optimal portfolio selection models with uncertain returns, Modern Applied Science 3 (2009) 76–81.
[15] P. Jana, T. Roy, S. Mazumder, Multi-objective Mean- variance-skewness model for portfolio optimization, Advanced Modeling and Optimization 9 (2007) 181–193.
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  • APA Style

    Shengguo Li, Jin Peng, Bo Zhang, Dan Ralescu. (2021). Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns. International Journal of Management and Fuzzy Systems, 7(3), 47-54. https://doi.org/10.11648/j.ijmfs.20210703.12

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    ACS Style

    Shengguo Li; Jin Peng; Bo Zhang; Dan Ralescu. Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns. Int. J. Manag. Fuzzy Syst. 2021, 7(3), 47-54. doi: 10.11648/j.ijmfs.20210703.12

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    AMA Style

    Shengguo Li, Jin Peng, Bo Zhang, Dan Ralescu. Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns. Int J Manag Fuzzy Syst. 2021;7(3):47-54. doi: 10.11648/j.ijmfs.20210703.12

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  • @article{10.11648/j.ijmfs.20210703.12,
      author = {Shengguo Li and Jin Peng and Bo Zhang and Dan Ralescu},
      title = {Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns},
      journal = {International Journal of Management and Fuzzy Systems},
      volume = {7},
      number = {3},
      pages = {47-54},
      doi = {10.11648/j.ijmfs.20210703.12},
      url = {https://doi.org/10.11648/j.ijmfs.20210703.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20210703.12},
      abstract = {Diversification portfolio selection problem is an important issue in uncertain economic environment. In this paper, this problem is discussed within the framework of uncertainty theory. First, an uncertain extension mean-variance diversification model is proposed, in which the mean is chosen as the objective function, and variance and proportion entropy as risk and diversity constraints. Then two variations are investigated on the purposes of minimizing the risk and maximizing the diversity measure, respectively. Furthermore, the corresponding analytical mathematical models are deduced via the convenient operational law of uncertain variables. Finally, several numerical examples are given to illustrate the modeling idea. The results showed that the diversification models had higher diversification than the uncertain mean-variance model. The proposed models provide a new method to make decision-making in uncertain portfolio selection problem.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns
    AU  - Shengguo Li
    AU  - Jin Peng
    AU  - Bo Zhang
    AU  - Dan Ralescu
    Y1  - 2021/08/23
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ijmfs.20210703.12
    DO  - 10.11648/j.ijmfs.20210703.12
    T2  - International Journal of Management and Fuzzy Systems
    JF  - International Journal of Management and Fuzzy Systems
    JO  - International Journal of Management and Fuzzy Systems
    SP  - 47
    EP  - 54
    PB  - Science Publishing Group
    SN  - 2575-4947
    UR  - https://doi.org/10.11648/j.ijmfs.20210703.12
    AB  - Diversification portfolio selection problem is an important issue in uncertain economic environment. In this paper, this problem is discussed within the framework of uncertainty theory. First, an uncertain extension mean-variance diversification model is proposed, in which the mean is chosen as the objective function, and variance and proportion entropy as risk and diversity constraints. Then two variations are investigated on the purposes of minimizing the risk and maximizing the diversity measure, respectively. Furthermore, the corresponding analytical mathematical models are deduced via the convenient operational law of uncertain variables. Finally, several numerical examples are given to illustrate the modeling idea. The results showed that the diversification models had higher diversification than the uncertain mean-variance model. The proposed models provide a new method to make decision-making in uncertain portfolio selection problem.
    VL  - 7
    IS  - 3
    ER  - 

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Author Information
  • Institute of Uncertain Systems, Huanggang Normal University, Huanggang, China

  • Institute of Uncertain Systems, Huanggang Normal University, Huanggang, China

  • School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, China

  • Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

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