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Influence of membership function’s shape on portfolio optimization results

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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
45--54
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
autor
  • Department of Applied Mathematics Poznan University of Economics and Business al. Niepodleglosci, 61-875 Poznan, Poland
Bibliografia
  • [1] H. Markowitz, Portfolio Selection, The Journal of Finance, vol.7, no.1, 1952, pp.77-91.
  • [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.
  • [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.
  • [4] X. Huang, Fuzzy chance-constrained portfolio selection, Applied Mathematics and Computation, vol. 177, no. 2, 2006, pp. 500–507.
  • [5] X. Huang, Mean-semivariance models for fuzzy portfolio selection, J.Comput. Appl. Math., vol. 217, no. 1, 2008, pp. 1–8.
  • [6] X. Huang, Mean-Entropy Models for Fuzzy Portfolio Selection, IEEE Transactions on Fuzzy Systems, vol. 16, 2008, pp. 1096–1101.
  • [7] X. Huang, Minimax mean-variance models for fuzzy portfolio selection, Soft Computing, vol. 15, no. 2,2010, pp. 251–260.
  • [8] X. Huang, Portfolio Analysis: From Probabilistic to Credibilistic and Uncertain Approaches, ser. Studies in Fuzziness and Soft Computing, Springer, 2010.
  • [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.
  • [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.
  • [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.
  • [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.
  • [13] B. Liu, Uncertainty Theory, ser. Studies in Fuzziness and Soft Computing. Springer, 2007.
  • [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.
  • [15] F. Wilcoxon, Individual comparisons by ranking methods, Biometrics Bulletin, vol. 1, no. 6, 1945, pp. 8083.
  • [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.
  • [17] J. Peng, Measuring Fuzzy Risk by Credibilistic Value at Risk, in International Conference on Innovative Computing, Information and Control, 2008.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
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Bibliografia
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bwmeta1.element.baztech-b04b83c8-7765-468e-96c1-87627d666335
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