# How the investor's risk preferences influence the optimal allocation in a credibilistic portfolio problem

## TL;DR

This paper explores how investors' risk preferences affect optimal portfolio allocation when risk is modeled as a fuzzy variable using Liu's credibility theory, introducing credibilistic expected utility and approximation formulas.

## Contribution

It introduces a credibilistic portfolio model with fuzzy risk, defining expected utility within Liu's credibility theory, and derives approximation formulas for optimal asset allocation.

## Key findings

- Derived formulas for optimal allocation involving credibilistic moments.
- Showed the influence of risk aversion, prudence, and temperance on portfolio choice.
- Extended classical portfolio theory to fuzzy risk scenarios.

## Abstract

A classical portfolio theory deals with finding the optimal proportion in which an agent invests a wealth in a risk-free asset and a probabilistic risky asset. Formulating and solving the problem depend on how the risk is represented and how, combined with the utility function defines a notion of expected utility. In this paper the risk is a fuzzy variable and the notion of expected utility is defined in the setting of Liu's credibility theory. Thus the portfolio choice problem is formulated as an optimization problem in which the objective function is a credibilistic expected utility. Different approximation calculation formulas for the optimal allocation of the credibilistic risky asset are proved. These formulas contain two types of parameters: various credibilistic moments associated with fuzzy variables (expected value, variance, skewness and kurtosis) and the risk aversion, prudence and temperance indicators of the utility function.