Territorial Risk Classification Using Spatially Dependent Frequency-Severity Models

In non-life insurance, territory-based risk classification is useful for various insurance operations including marketing, underwriting, ratemaking, etc. This paper proposes a spatially dependent frequency-severity modeling framework to produce territorial risk scores. The framework applies to the aggregated insurance claims where the frequency and severity components examine the occurrence rate and average size of insurance claims in each geographic unit, respectively. We employ the bivariate conditional autoregressive models to accommodate the spatial dependency in the frequency and severity components, as well as the cross-sectional association between the two components. Using a town-level claims data of automobile insurance in Massachusetts, we demonstrate applications of the model output–territorial risk scores–in ratemaking and market segmentation.