Classification of territory risk by generalized linear and generalized linear mixed models

Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation. Due to the optimality of insurance loss data groupings, clustering methods become the natural choice for such territory risk classification. In this work, spatially constrained clustering is first applied to insurance loss data to form rating territories. The generalized linear model (GLM) and generalized linear mixed model (GLMM) are then proposed to derive the risk relativities of obtained clusters. Each basic rating unit within the same cluster, namely Forward Sortation Area (FSA), takes the same risk relativity value as its cluster. The obtained risk relativities from GLM or GLMM are used to calculate the performance metrics, including RMSE, MAD, and Gini coefficients. The spatially constrained clustering and the risk relativity estimate help obtain a set of territory risk benchmarks used in rate filings to guide the rate regulation process.