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.

透过引入适用于计算灾难保险费率的新颖自适应鲁棒优化（ARO）框架并结合美国国家洪水保险计划（NFIP）的实际案例研究，本研究首次应用ARO方法进行灾难保险定价，并设计了保护历史和预测未来风险的方法，这样可以直接纳入气候变化所带来的加剧风险，最终提供了可行的费率设计和预测风险的保障，为保险费率建模提供了新的方法，且对政策制定者和相关利益相关者在建立对自然灾害不断增长的风险的抵御力方面提供了重要的工具。

灾难保险：一种自适应的鲁棒优化方法