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Possibilistic risk theory starts from the hypothesis that risk is modelled byfuzzy numbers. In particular, in a possibilistic portfolio choice problem, thereturn of a risky asset will be a fuzzy number. The expected utility operatorshave been introduced in a previous paper to build an abstract theory ofpossibilistic risk aversion. To each expected utility operator one canassociate a notion of possibilistic expected utility. Using this notion, wewill formulate in this very general context a possibilistic choice problem. Themain results of the paper are two approximate calculation formulas forcorresponding optimization problem. The first formula approximates the optimalallocation with respect to risk aversion and investor's prudence, as well asthe first three possibilistic moments. Besides these parameters, in the secondformula the temperance index of the utility function and the fourthpossibilistic moment appear.

A portfolio choice problem in the framework of expected utility operators