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Moments and Semi-Moments for fuzzy portfolios selection

Author

Listed:
  • 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)

Abstract

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
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00567012
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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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    Citations

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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, arXiv.org.
    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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