Despite its importance for insurance, there is almost no literature on statistical hail damage modeling. Statistical models for hailstorms exist, though they are generally not open-source, but no study appears to have developed a stochastic hail impact function. In this paper, we use hail-related insurance claim data to build a Gaussian line process with extreme marks to model both the geographical footprint of a hailstorm and the damage to buildings that hailstones can cause. We build a model for the claim counts and claim values, and compare it to the use of a benchmark deterministic hail impact function. Our model proves to be better than the benchmark at capturing hail spatial patterns and allows for localized and extreme damage, which is seen in the insurance data. The evaluation of both the claim counts and value predictions shows that performance is improved compared to the benchmark, especially for extreme damage. Our model appears to be the first to provide realistic estimates for hail damage to individual buildings.

翻译：尽管雹灾对保险业至关重要，但关于冰雹损害统计建模的文献几乎空白。现有针对冰雹风暴的统计模型通常并非开源，且尚未有研究开发出随机冰雹影响函数。本文利用与冰雹相关的保险索赔数据，构建了一个带有极端标记的高斯线过程，用于模拟冰雹风暴的地理足迹以及冰雹对建筑物造成的损害。我们建立了索赔次数与索赔金额的模型，并将其与基准确定性冰雹影响函数进行对比。结果表明，我们的模型在捕捉冰雹空间分布模式方面优于基准模型，并能刻画保险数据中出现的局部化与极端损害特征。对索赔次数与赔付金额预测的评估显示，模型性能较基准有所提升，尤其在极端损害情景中表现更优。该模型被认为是首个能为单体建筑提供现实冰雹损害估算的模型。