Estimating territory risk relativity using generalized linear mixed models and fuzzy C-Means clustering

Territory risk analysis has played an important role in auto insurance rate regulation. It aims to design rating territories from a set of basic rating units so that their respective risk relativities can be estimated to reflect the regional risk of insurance. In this work, spatially constrained clustering is first applied to insurance loss data to form such regions, using the forward sortation area (FSA) as a basic rating unit. The groupings of FSA by spatially constrained clustering reduce the insurance rate heterogeneity caused by smaller risk exposures. Furthermore, the generalized linear mixed model (GLMM) is proposed to derive the risk relativities of clusters and each FSA. In addition, as an alternative approach, fuzzy C-Means clustering is proposed to derive the risk relativity of FSA, and the obtained results are compared to the ones from GLMM. The spatially constrained clustering and risk relativity estimation help to retrieve a set of territory risk benchmarks used in rate filings within the regulation process. It also provides guidance for auto insurance companies on rate making.