Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

4 Issues per year

Open Access
Online
ISSN
2083-2567
See all formats and pricing
More options …

Influence Of Membership Function’s Shape On Portfolio Optimization Results

Aleksandra Rutkowska
  • Department of Applied Mathematics Poznan University of Economics and Business al. Niepodleglosci, 61-875 Poznan, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-01-13 | DOI: https://doi.org/10.1515/jaiscr-2016-0005

Abstract

Portfolio optimization, one of the most rapidly growing field of modern finance, is selection process, by which investor chooses the proportion of different securities and other assets to held. This paper studies the influence of membership function’s shape on the result of fuzzy portfolio optimization and focused on portfolio selection problem based on credibility measure. Four different shapes of the membership function are examined in the context of the most popular optimization problems: mean-variance, mean-semivariance, entropy minimization, value-at-risk minimization. The analysis takes into account both: the study of necessary and sufficient conditions for the existence of extremes, as well as the statistical inference about the differences based on simulation.

Keywords: fuzzy variable; membership function; fuzzy portfolio optimization

References

  • [1] H. Markowitz, Portfolio Selection, The Journal of Finance, vol.7, no.1, 1952, pp.77-91.Google Scholar

  • [2] B. Liu and Y.-K. Liu, Expected value of fuzzy variable and fuzzy expected value models, Fuzzy Systems, IEEE Transactions on, vol. 10, no. 4,2002, pp. 445–450.Google Scholar

  • [3] J. Peng, H.M.K., Mok, T., Wai-Man, Credibility programming approach to fuzzy portfolio selection problems, Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on, vol.4, 2005, pp.2523–2528.Google Scholar

  • [4] X. Huang, Fuzzy chance-constrained portfolio selection, Applied Mathematics and Computation, vol. 177, no. 2, 2006, pp. 500–507.Google Scholar

  • [5] X. Huang, Mean-semivariance models for fuzzy portfolio selection, J.Comput. Appl. Math., vol. 217, no. 1, 2008, pp. 1–8.Google Scholar

  • [6] X. Huang, Mean-Entropy Models for Fuzzy Portfolio Selection, IEEE Transactions on Fuzzy Systems, vol. 16, 2008, pp. 1096–1101.Web of ScienceCrossrefGoogle Scholar

  • [7] X. Huang, Minimax mean-variance models for fuzzy portfolio selection, Soft Computing, vol. 15, no. 2,2010, pp. 251–260.CrossrefWeb of ScienceGoogle Scholar

  • [8] X. Huang, Portfolio Analysis: From Probabilistic to Credibilistic and Uncertain Approaches, ser. Studies in Fuzziness and Soft Computing, Springer, 2010.CrossrefGoogle Scholar

  • [9] X. Li, Z. Qin, and S. Kar, Mean-variance-skewness model for portfolio selection with fuzzy returns, European Journal of Operational Research, vol. 202, no. 1, 2010, pp. 239–247.Google Scholar

  • [10] P. Koprinkova, Membership functions shape and its influence on the dynamical behaviour of fuzzy logic controller, Cybernetics and Systems: An International Journal, vol. 2, no. 31,1952, pp. 161–173.Google Scholar

  • [11] J. Marshall, M. Kazerani, and R. Shatshat, Investigation of membership function shapes in a fuzzy-controlled hvdc system, Industrial Electronics, 2006 IEEE International Symposium on, vol. 3, 2006, pp. 1800–1805.Google Scholar

  • [12] M. Multani, J. Ren, and V. Sood, Fuzzy logic (fl) controlled hvdc system-influence of shape ans distribution of membership functions (mfs) in Electrical and Computer Engineering (CCECE), 2010 23rd Canadian Conference on, 2010, pp. 1–7.Google Scholar

  • [13] B. Liu, Uncertainty Theory, ser. Studies in Fuzziness and Soft Computing. Springer, 2007.CrossrefGoogle Scholar

  • [14] P. Li and B. Liu, Entropy of credibility distributions for fuzzy variables, Fuzzy Systems, IEEE Transactions on, vol. 16, no. 1, 2008 pp. 123–129.Web of ScienceGoogle Scholar

  • [15] F. Wilcoxon, Individual comparisons by ranking methods, Biometrics Bulletin, vol. 1, no. 6, 1945, pp. 8083.Google Scholar

  • [16] S. Wang, J. Watada, and W. Pedrycz, Value-at-Risk-Based Two-Stage Fuzzy Facility Location Problems, IEEE Transactions on Industrial Informatics, vol. 5, 2009, pp. 465–482.Web of ScienceCrossrefGoogle Scholar

  • [17] J. Peng, Measuring Fuzzy Risk by Credibilistic Value at Risk, in International Conference on Innovative Computing, Information and Control, 2008.Google Scholar

About the article

Published Online: 2016-01-13

Published in Print: 2016-01-01


Citation Information: Journal of Artificial Intelligence and Soft Computing Research, Volume 6, Issue 1, Pages 45–54, ISSN (Online) 2083-2567, DOI: https://doi.org/10.1515/jaiscr-2016-0005.

Export Citation

© 2016 Academy of Management (SWSPiZ), Lodz. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Robert K. Nowicki and Janusz T. Starczewski
Information Sciences, 2017, Volume 414, Page 33

Comments (0)

Please log in or register to comment.
Log in