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Multi objective mean–variance–skewness model with Burg’s entropy and fuzzy return for portfolio optimization

Author

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  • Amritansu Ray

    (Indian Institute of Engineering Science and Technology (IIEST), Shibpur)

  • Sanat Kumar Majumder

    (Indian Institute of Engineering Science and Technology (IIEST), Shibpur)

Abstract

A new non-Shannon fuzzy Mean–Variance–Skewness-entropy model is proposed with stock returns are considered as triangular fuzzy numbers. The fuzzy stock portfolio selection models are presented with credibility theory that maximizes mean and skewness and minimizes portfolio variance and cross-entropy in terms of Burg. With addition of Burg’s entropy in the multi objective non linear models, focus is the generation of well diversified portfolios within the optimal allocation. For an imprecise capital market, this study facilitates a more reasonable investment decisions with four objective decision criteria including Burg’s entropy. Numerical examples with case studies are used to illustrate the entire method which can be efficiently used in practical purposes like national stock exchanges.

Suggested Citation

  • Amritansu Ray & Sanat Kumar Majumder, 2018. "Multi objective mean–variance–skewness model with Burg’s entropy and fuzzy return for portfolio optimization," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 107-133, March.
    • Handle: RePEc:spr:opsear:v:55:y:2018:i:1:d:10.1007_s12597-017-0311-z
    DOI: 10.1007/s12597-017-0311-z
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    References listed on IDEAS

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    1. Fred D. Arditti, 1967. "Risk And The Required Return On Equity," Journal of Finance, American Finance Association, vol. 22(1), pages 19-36, March.
    2. Prakash, Arun J. & Chang, Chun-Hao & Pactwa, Therese E., 2003. "Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets," Journal of Banking & Finance, Elsevier, vol. 27(7), pages 1375-1390, July.
    3. Gilmore, Claire G. & McManus, Ginette M. & Tezel, Ahmet, 2005. "Portfolio allocations and the emerging equity markets of Central Europe," Journal of Multinational Financial Management, Elsevier, vol. 15(3), pages 287-300, July.
    4. Sharpe, William F., 1971. "A Linear Programming Approximation for the General Portfolio Analysis Problem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1263-1275, December.
    5. Sadefo Kamdem, Jules & Tassak Deffo, Christian & Fono, Louis Aimé, 2012. "Moments and semi-moments for fuzzy portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 517-530.
    6. Ibbotson, Roger G., 1975. "Price performance of common stock new issues," Journal of Financial Economics, Elsevier, vol. 2(3), pages 235-272, September.
    7. Roy, T.K. & Maiti, M., 1997. "A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity," European Journal of Operational Research, Elsevier, vol. 99(2), pages 425-432, June.
    8. Akhter Mohiuddin Rather & V. N. Sastry & Arun Agarwal, 2017. "Stock market prediction and Portfolio selection models: a survey," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 558-579, September.
    9. Lin, Chang-Chun & Liu, Yi-Ting, 2008. "Genetic algorithms for portfolio selection problems with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 185(1), pages 393-404, February.
    10. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    11. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    12. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    13. Li, Xiang & Qin, Zhongfeng & Kar, Samarjit, 2010. "Mean-variance-skewness model for portfolio selection with fuzzy returns," European Journal of Operational Research, Elsevier, vol. 202(1), pages 239-247, April.
    14. Anil Bera & Sung Park, 2008. "Optimal Portfolio Diversification Using the Maximum Entropy Principle," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 484-512.
    15. Amritansu Ray & Sanat Kumar Majumder, 2016. "Concavity of maximum entropy through modified Burg's entropy subject to its prescribed mean," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 8(4), pages 393-405.
    16. Stone, Bernell K., 1973. "A Linear Programming Formulation of the General Portfolio Selection Problemâ€," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 621-636, September.
    17. Simkowitz, Michael A. & Beedles, William L., 1978. "Diversification in a Three-Moment World," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(5), pages 927-941, December.
    18. William F. Sharpe, 1967. "A Linear Programming Algorithm for Mutual Fund Portfolio Selection," Management Science, INFORMS, vol. 13(7), pages 499-510, March.
    19. Arditti, Fred D & Levy, Haim, 1975. "Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case," Journal of Finance, American Finance Association, vol. 30(3), pages 797-809, June.
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