Fitting generalised linear models to car claims data

Abstract

Generalised linear models (GLMs) overcome the limitations of Normal regression models since they can accommodate any distribution that is a member of the exponential family. These models allow transformation of the response variable through the canonical link function. This paper presents two GLMs to analyze a data set provided by a car insurance company. The first model is a lognormal regression model that relates claim size to a number of demographic, car-related and policy-related predictors and the second model is a Poisson regression model that relates the number of claims filed by a policy holder to these explanatory variables. An appropriate model that describes the aggregate claim amount in a portfolio of insurance contracts during a fixed period combines both claim size and number of claims through a compound Poisson distribution.