A numerical approach to utility functions in risk theory
Given the standard equilibrium model for an insurance market and sharing rules defining a feasible risk-exchange, we want to determine numerically the utility functions leading to the equilibrium. In the special case of two companies we approximate the sharing rules by piecewise linear functions and give an algorithm to compute piecewise quadratic utility functions which are solutions of the equilibrium model. We apply our method to compare some insurance contracts. For this we introduce the notion of acceptability of an insurance contract and a risk equivalence property based on utility theory. The numerical examples lead to interesting interpretations which give some insight in the considered insurance contracts.
scientific article; zbMATH DE number 3972045