Abstract：
Earthquake insurance is a critical risk management strategy that contributes to improving recovery and thus greater resilience of individuals. Insurance companies construct premiums without taking into account spatial correlations between insured assets. This leads to potentially underestimating the risk, and therefore the exceedance probability curve. We here propose a mixed-effects model to estimate losses per ward that is able to account for heteroskedasticity and spatial correlation between insured losses. Given the significant impact of earthquakes in New Zealand due to its particular geographical and demographic characteristics, the government has established a public insurance company that collects information about the insured buildings and any claims lodged. We thus develop a two-level variance component model that is based on earthquake losses observed in New Zealand between 2000 and 2021. The proposed model aims at capturing the variability at both the ward and territorial authority levels and includes independent variables, such as seismic hazard indicators, the number of usual residents, and the average dwelling value in the ward. Our model is able to detect spatial correlation in the losses at the ward level thus increasing its predictive power and making it possible to assess the effect of spatially correlated claims that may be considerable on the tail of loss distribution.
摘要：
地震保险是一项关键的风险管理战略，有助于改善恢复状况，从而提高个人的抵御能力。保险公司在不考虑保险资产之间的空间相关性的情况下构建保费。这导致潜在的低估风险，因此，超越概率曲线。我们在这里提出了一个混合效应模型来估计每个病房的损失，该模型能够解释保险损失之间的异方差和空间相关性。鉴于新西兰因其特殊的地理和人口特征而受到地震的重大影响，政府成立了一家公共保险公司，收集有关被保险建筑物和任何索赔的信息。因此，我们基于2000年至2021年在新西兰观测到的地震损失，开发了一个两级方差分量模型。拟议的模型旨在捕获病房和地区当局级别的可变性，并包括独立变量，如地震危险性指标，普通居民的数量，和病房的平均住宅价值。我们的模型能够检测病房级别损失的空间相关性，从而提高其预测能力，并有可能评估空间相关索赔的影响，这些索赔可能对损失分布的尾部相当大。
