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Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Author

Listed:
  • Christian Deffo Tassak

    (Université de Yaoundé I)

  • Jules Sadefo Kamdem

    (LAMETA CNRS UMR 5474 (Montpellier)
    Université de Guyane)

  • Louis Aimé Fono

    (Université de Douala)

  • Nicolas Gabriel Andjiga

    (Université de Yaoundé I)

Abstract

Peng et al (Int J Uncertain Fuzziness Knowl Based Syst 15:29–41, 2007) introduced, by means of the credibility measure, two dominance relations on fuzzy variables, namely the first- and the second-order dominances. In this paper, we characterize each of these dominance relations, and we justify that they satisfy six well-known properties of comparison methods. We propose a Game Theory approach for the determination of optimal portfolios when returns are fuzzy by introducing the set of best portfolios with respect to the first- and the second-order dominances. Based on the characterization of the first-order dominance, we numerically display some of the best portfolios of the classical set of portfolios of seven independent assets described by triangular fuzzy numbers.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-016-0164-5
    DOI: 10.1057/s41274-016-0164-5
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    1. 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.
    2. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, University Library of Munich, Germany, revised 07 Aug 2005.
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    5. Amelia Bilbao-Terol & Mar Arenas-Parra & Verónica Cañal-Fernández & Mariano Jiménez, 2016. "A sequential goal programming model with fuzzy hierarchies to sustainable and responsible portfolio selection problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1259-1273, October.
    6. 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.
    7. 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.
    8. Irina Georgescu & Jani Kinnunen, 2013. "A risk approach by credibility theory," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 399-416, December.
    9. 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.
    10. Michael J. Best & Robert R. Grauer, 1991. "Sensitivity Analysis for Mean-Variance Portfolio Problems," Management Science, INFORMS, vol. 37(8), pages 980-989, August.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

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