Mitigation of Data Scarcity in Crop Insurance Pricing by Exploiting Spatial Information: A Propagation-Separation Approach

鉴于作物保险在全球范围内的迅速扩张，保险合同的合理和准确定价方法对于为生产者、保险公司和政府维持可持续和可行的风险管理解决方案至关重要。与大多数保险形式不同的是，农业保险费率的制定受到作物数据在空间上相互关联且稀缺的困扰，通常最多只有50个观测结果。历史数据的缺乏可能导致损失分布的不正确估计，并将新的模型风险引入保险公司的决策问题。处理保险业数据短缺的一个实际方法是利用空间上邻近的数据来补充有限的历史观测，但这种收益率数据的纳入往往是临时的，缺乏正式的，健全的数学框架。混合来自不同分布的数据将导致逆向选择问题。因此，本研究项目的目标是开发一个正式的和严格的框架，利用空间信息，以减轻作物保险定价的数据稀缺。特别是，我们将采用和扩展自适应局部平滑模型（也称为简化-分离方法），该模型允许以更灵活和有效的方式识别局部均匀区域并估计共同分布的参数。该项目还将对不同的统计方法以及经验应用进行全面比较，以便更清楚地了解空间信息发挥最大作用的条件。

In view of the rapid expansion of crop insurance worldwide, a sound and accurate pricing approach of insurance contracts is of utmost importance to maintain sustainable and viable risk management solutions for producers, insurers and governments. Unlike most forms of insurance where sufficient information exists to estimate reliable loss distributions and insurance premiums, agricultural insurance ratemaking is plagued by the fact that crop data are spatially correlated and scarce, usually 50 observations at most. The lack of historic data may lead to incorrect estimations of loss distributions and introduces a new model risk into the insurer's decision problem. A practical approach to deal with data scarcity in insurance industry is to utilize spatially nearby data to complement the limited historical observations, but the incorporation of such yield data is often on an ad hoc basis, lacking a formal, sound mathematical framework. Mixing data from dissimilar distributions would lead to adverse selection problems. Therefore, the objective of this research project is to develop a formal and rigorous framework to exploit the spatial information for mitigating data scarcity in crop insurance pricing. Particularly, we will adopt and extend the adaptive local smoothing model (also referred to the Propagation-Separation approach) that allows to identify local homogeneous areas and estimate parameters of the common distribution in a more flexible and efficient way. The project will further provide a comprehensive comparison of different statistical methods as well as empirical applications to draw a clearer picture of the conditions under which spatial information can be most helpful.