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

Author

Listed:
  • Christian Deffo Tassak

    (UY1 - Université de Yaoundé I)

  • Jules Sadefo-Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier, UG - Université de Guyane)

  • Louis Aimé Fono

    (Université de Douala)

  • Nicolas Gabriel Andjiga

    (UY1 - Université de Yaoundé I, École normale supérieure [ENS] - Yaoundé 1)

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, 2018. "Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns," Post-Print hal-02901704, HAL.
    • Handle: RePEc:hal:journl:hal-02901704
    DOI: 10.1057/s41274-016-0164-5
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    2. 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.
    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.
    5. 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.

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