Geographical Ratings with Spatial Random Effects in a Two-Part Model

By Chun Wang, Elizabeth D Schifano, Jun Yan

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Rating areas are commonly used to capture unexplained geographical variability of claims in insurance pricing. A new method for defining rating areas is proposed using a two-part generalized geoadditive model that models spatial effects smoothly using Gaussian Markov random fields. The first part handles zero/nonzero expenses in a logistic model; the second handles nonzero expenses (on log-scale) in a linear model. Both models are fit with R package INLA for Bayesian infer-ences. The resulting spatial effects are used to construct more representative ratings. The methodology is illustrated with simulated data based on zipcode areas, but modeled on zipcode- or county-level.

Keywords Geoadditive model; INLA; rating area; territory analysis


Wang, Chun, Elizabeth D Schifano, and Jun Yan, "Geographical Ratings with Spatial Random Effects in a Two-Part Model," Variance 13:1, 2020, pp. 141-160.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.