Utility Indifference Pricing of Insurance Catastrophe Derivatives

TL;DR

This paper develops a utility indifference pricing model for insurance catastrophe derivatives, incorporating a new loss index and claims process, and solves the associated stochastic optimization using advanced Markov process techniques.

Contribution

It introduces a novel model for an insurance loss index and claims process, applying utility indifference pricing to catastrophe derivatives with a new numerical solution approach.

Findings

Numerical results demonstrate the model's effectiveness.

The pricing method captures both ordinary and catastrophe losses.

The approach provides practical insights for insurance risk management.

Abstract

We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catastrophe derivative by the method of utility indifference pricing. The associated stochastic optimization problem is treated by techniques for piecewise deterministic Markov processes. A numerical study illustrates our results.