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Risks 2019, 7(2), 42; https://doi.org/10.3390/risks7020042

Defining Geographical Rating Territories in Auto Insurance Regulation by Spatially Constrained Clustering

1
Ted Rogers School of Management, Ryerson University, Toronto, ON M5B 2K3, Canada
2
Mathematics and Statistics, University of Guelph, Guelph, ON N1G 2W1, Canada
Received: 11 March 2019 / Accepted: 13 April 2019 / Published: 17 April 2019
PDF [1830 KB, uploaded 17 April 2019]

Abstract

Territory design and analysis using geographical loss cost are a key aspect in auto insurance rate regulation. The major objective of this work is to study the design of geographical rating territories by maximizing the within-group homogeneity, as well as maximizing the among-group heterogeneity from statistical perspectives, while maximizing the actuarial equity of pure premium, as required by insurance regulation. To achieve this goal, the spatially-constrained clustering of industry level loss cost was investigated. Within this study, in order to meet the contiguity, which is a legal requirement on the design of geographical rating territories, a clustering approach based on Delaunay triangulation is proposed. Furthermore, an entropy-based approach was introduced to quantify the homogeneity of clusters, while both the elbow method and the gap statistic are used to determine the initial number of clusters. This study illustrated the usefulness of the spatially-constrained clustering approach in defining geographical rating territories for insurance rate regulation purposes. The significance of this work is to provide a new solution for better designing geographical rating territories. The proposed method can be useful for other demographical data analysis because of the similar nature of the spatial constraint.
Keywords: rate-making; rating territory; insurance rate filing; spatially-constrained clustering; entropy methods; clustering rate-making; rating territory; insurance rate filing; spatially-constrained clustering; entropy methods; clustering
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Xie, S. Defining Geographical Rating Territories in Auto Insurance Regulation by Spatially Constrained Clustering. Risks 2019, 7, 42.

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