Catastrophe Insurance Pricing: An Adaptive Robust Optimization Approach

The escalating frequency and severity of natural disasters, exacerbated by climate change, underscores the critical role of insurance in facilitating recovery and promoting investments in risk reduction. The paper introduces a novel adaptive robust optimization (ARO) framework tailored for the calculation of catastrophe insurance premiums, with a case study applied to the US National Flood Insurance Program. To the best of our knowledge, it is the first time an ARO approach has been applied to 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 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 that ARO models with conservative parameter values achieve a low number of insolvent states with the least insurance premium charged. Overall, optimization frameworks offer versatility and generalizability, making them adaptable to a variety of natural disaster scenarios, such as wildfires and droughts, among others. 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.