Optimal intertemporal risk allocation applied to insurance pricing

TL;DR

This paper introduces a novel, practical method for multi-period insurance pricing by combining utility indifference pricing with optimal risk allocation, aligning well with traditional risk loadings.

Contribution

It develops a new premium calculation method for multi-period insurance using exponential utility, characterized by a first order condition, and demonstrates its simplicity and numerical effectiveness.

Findings

Numerical results align with traditional risk loadings.

The method is simple and easily implemented.

Suggests a new implied utility approach to insurance pricing.

Abstract

We present a general approach to the pricing of products in finance and insurance in the multi-period setting. It is a combination of the utility indifference pricing and optimal intertemporal risk allocation. We give a characterization of the optimal intertemporal risk allocation by a first order condition. Applying this result to the exponential utility function, we obtain an essentially new type of premium calculation method for a popular type of multi-period insurance contract. This method is simple and can be easily implemented numerically. We see that the results of numerical calculations are well coincident with the risk loading level determined by traditional practices. The results also suggest a possible implied utility approach to insurance pricing.