# A portfolio choice problem in the framework of expected utility operators

## TL;DR

This paper develops a general framework for possibilistic portfolio choice using expected utility operators, providing approximate formulas for optimal asset allocation based on fuzzy risk modeling and utility parameters.

## Contribution

It introduces two approximation formulas for possibilistic portfolio optimization that incorporate utility features and higher-order fuzzy moments.

## Key findings

- First formula uses risk aversion, prudence, and first three moments.
- Second formula includes temperance index and fourth moment.
- Formulas enable practical approximation of optimal investment in fuzzy risk context.

## Abstract

Possibilistic risk theory starts from the hypothesis that risk is modelled 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 a notion of possibilistic expected utility. Using this notion, we will formulate in this very general context a possibilistic choice problem. The main results of the paper are two approximate calculation formulas for 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.