Changing climate and technology can often lead to nonstationary losses across both time and space for a variety of insurance lines including property, catastrophe, health, and life. As a result, naive estimation of premium rates using past losses will tend to be biased. We present three successively flexible data‐driven methodologies to nonparametrically smooth across both space and time simultaneously, thereby appropriately incorporating possibly nonidentically distributed data into the rating process. We apply these methodologies in estimating U.S. crop insurance premium rates. Crop insurance, with global premiums totaling $4.1 trillion in 2018, is an interesting application as losses exhibit both temporal and spatial nonstationarity. We find significant borrowing of information across both time and space. We also find all three methodologies improve both the stability and accuracy of crop insurance premium rates. The proposed methods may be of relevance for other lines of insurance characterized by spatial and/or temporal nonstationary losses.

中文翻译：

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跨时空同时借用信息以为保险合同定价：用于对农作物保单进行评级的应用

气候和技术的变化通常会导致财产，灾难，健康和人寿等各种保险项目在时间和空间上造成不稳定损失。结果，使用过去的损失对保险费率的天真的估计将趋于偏差。我们提出了三种连续灵活的数据驱动方法，以同时在空间和时间上进行非参数平滑，从而将可能分布不均的数据适当地纳入了评估过程。我们将这些方法应用于估计美国农作物保险费率。作物保险在2018年的全球保费总额为4.1万亿美元，是一项有趣的应用，因为损失表现出时间和空间的非平稳性。我们发现在时间和空间上都大量借用了信息。我们还发现，所有这三种方法都可以提高作物保险费率的稳定性和准确性。所提出的方法可能与以空间和/或时间上的非平稳损失为特征的其他保险类别有关。