Asymptotic Analysis of Optimal Diversification in Catastrophe Risk Pooling

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.