A Portfolio Choice Problem in the Framework of Expected Utility Operators

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 the...

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Bibliographic Details
Published inMathematics (Basel) Vol. 7; no. 8; p. 669
Main Authors Georgescu, Irina, Fono, Louis Aimé
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 2019
Subjects
Decision theory
Expected utility
expected utility operators
Expected values
Food science
Fuzzy systems
Operators (mathematics)
Optimization
portfolio choice problem
possibilistic moments
Random variables
Risk allocation
Utility functions
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7080669