Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns

Shengguo Li; Jin Peng; Bo Zhang; Dan Ralescu

doi:doi:10.11648/j.ijmfs.20210703.12

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Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns

Shengguo Li, Jin Peng, Bo Zhang, Dan Ralescu

Published in International Journal of Management and Fuzzy Systems (Volume 7, Issue 3)

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), 2024. Published by Science Publishing Group

Keywords

Portfolio Selection, Uncertain Variable, Entropy, Uncertainty Modeling

References

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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

Shengguo Li

Institute of Uncertain Systems, Huanggang Normal University, Huanggang, China
Jin Peng

Institute of Uncertain Systems, Huanggang Normal University, Huanggang, China
Bo Zhang

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

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

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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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