Rating endorsements using generalized linear models**

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.