Generalized Linear Models for Insurance Pricing

GLM Framework

Generalized linear models (GLMs) are the workhorse of modern insurance pricing. A GLM consists of three components: a random component (the distribution of the response variable), a systematic component (a linear predictor of rating factors), and a link function connecting them. For insurance frequency models, actuaries typically use a Poisson or negative binomial distribution with a log link. For severity models, a gamma distribution with a log link is common. The multiplicative structure that results from the log link aligns naturally with how insurance rates are built from base rates and relativities.

Practical Considerations

Fitting GLMs for insurance pricing requires careful attention to several issues. Exposure must be included as an offset variable in frequency models. Categorical variables with many levels (like territory) may need grouping or regularization. Interaction effects between rating variables should be tested systematically. Model validation involves comparing observed and predicted loss ratios across rating variable levels, using lift charts, and performing out-of-sample testing. Actuaries must also consider regulatory requirements, as some jurisdictions restrict which rating variables may be used or require specific forms for rate filings.