Catastrophe Insurance: An Adaptive Robust Optimization Approach

TL;DR

This paper presents a novel Adaptive Robust Optimization framework for catastrophe insurance pricing, incorporating climate change-induced risks and machine learning predictions, demonstrated through a US flood insurance case study.

Contribution

It introduces the first application of ARO to disaster insurance pricing, integrating emerging risks and machine learning insights for more resilient premium calculations.

Findings

ARO models achieve low insolvency rates with minimal premiums

Optimization models effectively balance coverage and surplus

Framework adaptable to various natural disaster scenarios

Abstract

The escalating frequency and severity of natural disasters, exacerbated by climate change, underscore the critical role of insurance in facilitating recovery and promoting investments in risk reduction. This work introduces a novel Adaptive Robust Optimization (ARO) framework tailored for the calculation of catastrophe insurance premiums, with a case study applied to the United States National Flood Insurance Program (NFIP). To the best of our knowledge, it is the first time an ARO approach has been applied to for disaster insurance pricing. Our methodology is designed to protect against both historical and emerging risks, the latter predicted by machine learning models, thus directly incorporating amplified risks induced by climate change. Using the US flood insurance data as a case study, optimization models demonstrate effectiveness in covering losses and produce surpluses, with a smooth balance transition through parameter fine-tuning. Among tested optimization models, results show ARO models with conservative parameter values achieving low number of insolvent states with the least insurance premium charged. Overall, optimization frameworks offer versatility and generalizability, making it adaptable to a variety of natural disaster scenarios, such as wildfires, droughts, etc. This work not only advances the field of insurance premium modeling but also serves as a vital tool for policymakers and stakeholders in building resilience to the growing risks of natural catastrophes.