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Moments and semi-moments for fuzzy portfolio selection

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  • Sadefo Kamdem, Jules
  • Tassak Deffo, Christian
  • Fono, Louis Aimé

Abstract

The aim of this paper is to consider the moments and the semi-moments for credibilistic portfolio selection with fuzzy risk factors (for example trapezoidal risk factors). In order to measure the leptokurtocity of credibilistic portfolio return, notions of moments (for example Kurtosis) and semi-moments (for example Semi-kurtosis) for credibilistic portfolios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean–variance–skewness model for credibilistic portfolio, the mean–variance–skewness–semi-kurtosis is presented and its four corresponding variants are also considered. We display numerical examples for our optimization models.

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  • 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.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:517-530
    DOI: 10.1016/j.insmatheco.2012.07.003
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    1. Walter Briec & Kristiaan Kerstens & Octave Jokung, 2007. "Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach," Management Science, INFORMS, vol. 53(1), pages 135-149, January.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. 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.
    4. Tanaka, Hideo & Guo, Peijun, 1999. "Portfolio selection based on upper and lower exponential possibility distributions," European Journal of Operational Research, Elsevier, vol. 114(1), pages 115-126, April.
    5. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    6. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
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    Cited by:

    1. Georgescu Irina & Kinnunen Jani, 2019. "How the Investor’s Risk Preferences Influence the Optimal Allocation in a Credibilistic Portfolio Problem," Journal of Systems Science and Information, De Gruyter, vol. 7(4), pages 317-329, August.
    2. Christian Deffo Tassak & Jules Sadefo Kamdem & Louis Aimé Fono & Nicolas Gabriel Andjiga, 2017. "Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1491-1502, December.
    3. Yue, Wei & Wang, Yuping, 2017. "A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 124-140.
    4. Yin-Yin Huang & I-Fei Chen & Chien-Liang Chiu & Ruey-Chyn Tsaur, 2021. "Adjustable Security Proportions in the Fuzzy Portfolio Selection under Guaranteed Return Rates," Mathematics, MDPI, vol. 9(23), pages 1-18, November.
    5. Liu, Yong-Jun & Zhang, Wei-Guo, 2013. "Fuzzy portfolio optimization model under real constraints," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 704-711.
    6. Justin Dzuche & Christian Deffo Tassak & Jules Sadefo-Kamdem & Louis Aimé Fono, 2019. "On Two Dominances of Fuzzy Variables based on a Parametric Fuzzy Measure and Application to Portfolio Selection with Fuzzy Return," Working Papers hal-02433438, HAL.
    7. Justin Dzuche & Christian Deffo Tassak & Jules Sadefo Kamdem & Louis Aimé Fono, 2021. "On two dominances of fuzzy variables based on a parametrized fuzzy measure and application to portfolio selection with fuzzy return," Annals of Operations Research, Springer, vol. 300(2), pages 355-368, May.
    8. Chen, Wei, 2015. "Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 125-139.
    9. Christian Tassak & Jules Sadefo-Kamdem & Louis Aimé Fono, 2012. "Dominances on fuzzy variables based on credibility measure," Working Papers hal-00796215, HAL.
    10. Justin Dzuche & Christian Deffo Tassak & Jules Sadefo-Kamdem & Louis Aimé Fono, 2019. "On the first moments and semi-moments of fuzzy variables based on a new measure and application for portfolio selection with fuzzy returns," Working Papers hal-02433463, HAL.
    11. Irina Georgescu & Louis Aimé Fono, 2019. "A Portfolio Choice Problem in the Framework of Expected Utility Operators," Mathematics, MDPI, vol. 7(8), pages 1-16, July.
    12. Christian Deffo Tassak & Louis Aimé Fono & Jules Sadefo-Kamdem, 2019. "Fuzzy lower partial moment and Mean-risk Dominance: An application for poverty Measurement," Working Papers hal-02433422, HAL.
    13. 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.
    14. Michał Boczek, 2015. "On some risk measures," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 37, pages 323-338.

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