Mean-Entropy-Skewness Fuzzy Portfolio Selection by Credibility Theory Approach

  • Rupak Bhattacharyya
  • Mohuya B. Kar
  • Samarjit Kar
  • Dwijesh Dutta Majumder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5909)


In this paper fuzzy mean-entropy-skewness models are proposed for optimal portfolio selection. Entropy is favored as a measure of risk as it is free from dependence on symmetric probability distribution. Credibility theory is applied to evaluate fuzzy mean, skewness and entropy. Hybrid intelligence algorithm is used for simulation. Numerical examples are given in favor of each of the models.


Fuzzy portfolio selection problem Credibility theory Entropy Skewness Mean- entropy- skewness model Hybrid intelligence algorithm 


  1. 1.
    Philippatos, G.C., Wilson, C.J.: Entropy, market risk and selection of efficient portfolios. Applied Economics 4, 209–220 (1972)CrossRefGoogle Scholar
  2. 2.
    Philippatos, G.C., Gressis, N.: Conditions of equivalence among E–V, SSD, and E–H portfolio selection criteria: The case for uniform, normal and lognormal distributions. Manag. Sci. 21, 617–625 (1975)zbMATHCrossRefGoogle Scholar
  3. 3.
    Nawrocki, D.N., Harding, W.H.: State-value weighted entropy as a measure of investment risk. Appl. Econ. 18, 411–419 (1986)CrossRefGoogle Scholar
  4. 4.
    Simonelli, M.R.: Indeterminacy in portfolio selection. Eur. J. Oper. Res. 163, 170–176 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Huang, X.: Mean-entropy models for fuzzy portfolio selection. IEEE Transactions on Fuzzy Systems 16(4), 1096–1101 (2008)CrossRefGoogle Scholar
  6. 6.
    Qin, Z., Li, X., Ji, X.: Portfolio selection based on fuzzy cross-entropy. Journal of Computational and Applied Mathematics 228(1), 188–196 (2009)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Markowitz, H.: Portfolio selection. J. Finance 7, 77–91 (1952)CrossRefGoogle Scholar
  8. 8.
    Lai, T.: Portfolio selection with skewness: a multiple – objective approach. Review of the Quantitative Finance and Accounting 1, 293–305 (1991)CrossRefGoogle Scholar
  9. 9.
    Konno, H., Suzuki, K.: A mean-variance-skewness optimization model. Journal of the Operations Research Society of Japan 38, 137–187 (1995)Google Scholar
  10. 10.
    Chunhachinda, P., Dandapani, P., Hamid, S., Prakash, A.J.: Portfolio selection and skewness: evidence from international stock markets. Journal of Banking and Finance 21, 143–167 (1997)CrossRefGoogle Scholar
  11. 11.
    Liu, S.C., Wang, S.Y., Qiu, W.H.: A mean- variance- skewness model for portfolio selection with transaction costs. International Journal of System Science 34, 255–262 (2003)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Briec, W., Kerstens, K., Jokung, O.: Mean-variance- skewness portfolio performance gauging: a general shortage function and dual approach. Management Science 53, 135–149 (2007)CrossRefGoogle Scholar
  13. 13.
    Ramaswamy, S.: Portfolio selection using fuzzy decision theory. Working paper of Bank for International Settlements 59 (1998)Google Scholar
  14. 14.
    Inuiguchi, M., Ramik, J.: Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems 111, 3–28 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Li, X., Qin, Z., Kar, S.: Mean-variance-skewness model for portfolio selection with fuzzy returns. European Journal of Operational Research (2009), doi:10.1016/j.ejor.2009.05.003.Google Scholar
  16. 16.
    Li, P., Liu, B.: Entropy of credibility distributions for fuzzy variables. IEEE Transactions for Fuzzy Systems 16(1), 123–129 (2008)CrossRefGoogle Scholar
  17. 17.
    Liu, B.: Uncertainty Theory, 3rd edn.,
  18. 18.
    Huang, X.: Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation 177, 500–507 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Huang, X.: Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics 217, 1–8 (2008)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rupak Bhattacharyya
    • 1
  • Mohuya B. Kar
    • 2
  • Samarjit Kar
    • 1
  • Dwijesh Dutta Majumder
    • 3
  1. 1.Department of MathematicsNational Institute of TechnologyDurgapurIndia
  2. 2.Department of C.S.E.Heritage Institute of TechnologyKolkataIndia
  3. 3.Electronics & Communication Science UnitIndian Statistical InstituteKolkataIndia

Personalised recommendations