Using Cluster Analysis to Define Geographical Rating Territories

Geographic risk is a primary rating variable for personal lines insurance in the United States. Creating homogeneous groupings of geographic areas is the goal in defining rating territories. One methodology that can be used for creating these groupings with similar exposure to the risk of insurance losses is cluster analysis. This paper gives a description of an application to define rating territories using a k-means partition cluster analysis. Several of the key decisions made during the analysis are detailed including the following: the choice of building blocks, what variables to cluster on, choice of complement of credibility, and what clustering method is appropriate. In addition to the choice I made for each of these, I offer alternative choices that should be considered throughout the process. The method outlined here is based on Michael J Miller’s presentation at the 2004 CAS Ratemaking Seminar titled “Determination of Geographical Territories.” The measure of homogeneity used for this analysis is the within cluster variance as a percentage of the total variance. It will be shown that for the particular analysis that I describe in this paper, the within cluster variance as a percentage of the total variance was significantly reduced from 29.4% to 5.3%. This was also a more powerful result in comparison to the territory definitions of any of the major writers in this state.

Keywords. Rating territory definitions, cluster analysis, personal lines.