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Moments and Semi-Moments for fuzzy portfolios selection


  • Louis Aimé Fono

    () (MASS - Laboratoire de Mathématiques appliquées aux Sciences Sociales - Université de Douala)

  • Jules Sadefo Kamdem

    () (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UM3 - Université Paul-Valéry - Montpellier 3 - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - INRA Montpellier - Institut national de la recherche agronomique [Montpellier] - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

  • Christian Tassak

    (MASS - Laboratoire de Mathématiques appliquées aux Sciences Sociales - Université de Douala)


The aim of this paper is to consider the moments and the semi-moments (i.e semi-kurtosis) for portfolio selection with fuzzy risk factors (i.e. trapezoidal risk factors). In order to measure the leptokurtocity of fuzzy portfolio return, notions of moments (i.e. Kurtosis) kurtosis and semi-moments(i.e. Semi-kurtosis) for fuzzy port- folios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-semivariance-skewness model for fuzzy portfolio, the mean-semivariance-skewness- semikurtosis is presented and its four corresponding variants are also considered. We briefly designed the genetic algorithm integrating fuzzy simulation for our optimization models.

Suggested Citation

  • Louis Aimé Fono & Jules Sadefo Kamdem & Christian Tassak, 2011. "Moments and Semi-Moments for fuzzy portfolios selection," Working Papers hal-00567012, HAL.
  • Handle: RePEc:hal:wpaper:hal-00567012
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    References listed on IDEAS

    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. 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.
    2. repec:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-016-0164-5 is not listed on IDEAS
    3. repec:spr:opsear:v:55:y:2018:i:1:d:10.1007_s12597-017-0311-z is not listed on IDEAS
    4. 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.
    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. Christian Tassak & Jules Sadefo Kamdem & Louis Aimé Fono, 2012. "Dominances on fuzzy variables based on credibility measure," Working Papers hal-00796215, HAL.
    7. Irina Georgescu & Jani Kinnunen, 2019. "How the investor's risk preferences influence the optimal allocation in a credibilistic portfolio problem," Papers 1901.08986,
    8. 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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