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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.

Suggested Citation

  • 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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    References listed on IDEAS

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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. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," Review of Economic Studies, Oxford University Press, vol. 37(4), pages 537-542.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. 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.
    5. 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.
    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. 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.
    2. 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.
    3. 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.
    4. Christian Tassak & Jules Sadefo Kamdem & Louis Aimé Fono, 2012. "Dominances on fuzzy variables based on credibility measure," Working Papers hal-00796215, HAL.
    5. 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.
    6. Irina Georgescu & Jani Kinnunen, 2019. "How the investor's risk preferences influence the optimal allocation in a credibilistic portfolio problem," Papers 1901.08986, arXiv.org.
    7. repec:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-016-0164-5 is not listed on IDEAS
    8. repec:spr:opsear:v:55:y:2018:i:1:d:10.1007_s12597-017-0311-z is not listed on IDEAS

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