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A Portfolio Choice Problem in the Framework of Expected Utility Operators

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  • Irina Georgescu

    (Academy of Economic Studies, Department of Economic Informatics and Cybernetics, Bucharest University of Economics, Piaţa Romana No 6 R 70167, Oficiul Postal 22, 70167 Bucharest, Romania)

  • Louis Aimé Fono

    (Laboratory of Mathematics and Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Douala, Douala P.O. Box 24157, Cameroon)

Abstract

Possibilistic risk theory starts from the hypothesis that risk is modeled by fuzzy numbers. In particular, in a possibilistic portfolio choice problem, the return of a risky asset will be a fuzzy number. The expected utility operators have been introduced in a previous paper to build an abstract theory of possibilistic risk aversion. To each expected utility operator, one can associate the notion of possibilistic expected utility. Using this notion, we will formulate in this very general context a possibilistic portfolio choice problem. The main results of the paper are two approximate calculation formulas for the corresponding optimization problem. The first formula approximates the optimal allocation with respect to risk aversion and investor’s prudence, as well as the first three possibilistic moments. Besides these parameters, in the second formula, the temperance index of the utility function and the fourth possibilistic moment appear.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:669-:d:252058
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    References listed on IDEAS

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    1. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
    2. Ñíguez, Trino-Manuel & Paya, Ivan & Peel, David, 2016. "Pure higher-order effects in the portfolio choice model," Finance Research Letters, Elsevier, vol. 19(C), pages 255-260.
    3. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    4. 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.
    5. Irina Georgescu & Jani Kinnunen, 2016. "Mixed Models For Risk Aversion, Optimal Saving, And Prudence," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 21(2), pages 47-70, November.
    6. Fama, Eugene F, 1970. "Multiperiod Consumption-Investment Decisions," American Economic Review, American Economic Association, vol. 60(1), pages 163-174, March.
    7. Irina Georgescu & Adolfo Cristóbal-Campoamor & Ana Mª Lucia-Casademunt, 2017. "A Possibilistic and Probabilistic Approach to Precautionary Saving," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 64(3), pages 273-295.
    8. 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.
    9. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, April.
    10. Irina Georgescu & Jani Kinnunen, 2016. "Mixed Models For Risk Aversion, Optimal Saving, And Prudence," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 21(2), pages 47-70, November.
    11. Irina Georgescu & Adolfo CristóbalCampoamor & Ana Mª LuciaCasademunt, 2017. "A Possibilistic and Probabilistic Approach to Precautionary Saving," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 64(3), pages 273-295, June.
    12. Georgescu, Irina, 2008. "Possibilistic Risk Aversion," Working Papers 476, IAMSR, Åbo Akademi.
    13. Irina Georgescu, 2018. "The Effect of Prudence on the Optimal Allocation in Possibilistic and Mixed Models," Mathematics, MDPI, vol. 6(8), pages 1-19, August.
    14. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
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    Cited by:

    1. Marcel-Ioan Boloș & Ioana-Alexandra Bradea & Camelia Delcea, 2021. "Optimization of Financial Asset Neutrosophic Portfolios," Mathematics, MDPI, vol. 9(11), pages 1-36, May.
    2. Irina Georgescu, 2019. "Expected utility operators and coinsurance problem," Papers 1908.06927, arXiv.org.

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