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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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    2. Irina Georgescu, 2019. "Expected utility operators and coinsurance problem," Papers 1908.06927, arXiv.org.

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