Asymptotic Analysis of Optimal Diversification in Catastrophe Risk Pooling

TL;DR

This paper develops an asymptotic approach to optimize catastrophe risk pooling, providing a practical approximation to complex high-dimensional optimization problems, validated through simulations and empirical data.

Contribution

It introduces an asymptotic analysis method to derive near-optimal catastrophe risk pools, simplifying complex optimization in insurance risk management.

Findings

Asymptotically optimal pools closely match practical optimal pools in simulations.

The framework effectively approximates high-dimensional optimization problems.

Empirical analysis demonstrates practical applicability with U.S. flood insurance data.

Abstract

Catastrophe risk has long been recognized to pose a serious threat to the insurance sector. Catastrophe risk pooling offers an effective way to diversify losses arising from catastrophic events. In this paper, we investigate a structure of catastrophe risk pool and optimize it so that participants can attain the maximum diversification benefit from joining the pool. Determining the practical optimal pool entails solving a high-dimensional optimization problem, for which analytical solutions are typically unavailable and numerical methods can be computationally intensive and potentially unreliable. To address this challenge, we evaluate the diversification benefit in the limit and use it to derive an asymptotically optimal pool which approximates the practical optimal pool. Through simulation studies, we show that the asymptotically optimal pool provides an accurate and reliable approximation to the practical optimal pool. We also conduct an empirical analysis using data from the U.S. National Flood Insurance Program to illustrate how the framework can be applied in practice.