Expected utility operators and coinsurance problem

TL;DR

This paper extends the expected utility framework to a possibilistic setting using fuzzy numbers, analyzing optimal coinsurance rates and deriving formulas based on utility functions and fuzzy risk measures.

Contribution

It formulates a coinsurance problem within the expected utility operator framework using fuzzy numbers, providing properties and approximation formulas for optimal coinsurance rates.

Findings

Derived formulas for optimal coinsurance rates under various utility functions.

Established properties of the optimal T-coinsurance rate in the fuzzy setting.

Provided approximation methods based on the Arrow-Pratt index and fuzzy number characteristics.

Abstract

The expected utility operators introduced in a previous paper, offer a framework for a general risk aversion theory, in which risk is modelled by a fuzzy number $A$. In this paper we formulate a coinsurance problem in the possibilistic setting defined by an expected utility operator $T$. Some properties of the optimal saving $T$-coinsurance rate are proved and an approximate calculation formula of this is established with respect to the Arrow-Pratt index of the utility function of the policyholder, as well as the expected value and the variance of a fuzzy number $A$. Various formulas of the optimal $T$-coinsurance rate are deduced for a few expected utility operators in case of a triangular fuzzy number and of some HARA and CRRA-type utility functions.