Rating Endorsements Using Generalized Linear Models

By Edward W. Frees, Gee Lee

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Insurance policies often contain optional insurance coverages known as endorsements. Because these additional coverages are typically inexpensive relative to primary coverages and data can be sparse (coverages are optional), rating of endorsements is often done in an ad hoc manner after a primary analysis has been conducted. This paper describes a study of the Wisconsin Local Government Property Insurance Fund where it is desirable to have a formal mechanism for rating endorsements. Our goal is to provide prediction algorithms that are transparent and that promote equity among policyholders by determining rates that reflect the appropriate level and amount of uncertainty of each risk. To accommodate potentially conflicting goals of data complexity and algorithmic transparency, we utilize shrinkage techniques to moderate the effects of endorsements with penalized likelihoods. We find that the rating algorithms using shrinkage techniques have a predictive accuracy that are comparable to unbiased generalized linear model techniques and provide relativities for endorsements that are consistent with sound economic, risk management, and actuarial practice.

Keywords: Tweedie distribution, shrinkage estimation, insurance pricing


Frees, Edward W., and Gee Lee, "Rating Endorsements Using Generalized Linear Models," Variance 10:1, 2016, pp. 51-74.

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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.