Generalized Linear Models in Actuarial Work

Abstract

THE use of classical linear models in actuarial work is not new. Such models have become an established part of the description of claim frequency rates and average claim costs in motor insurance—as evidenced by a number of papers, including Johnson and Hey, Grimes, Bennett, Baxter et al. and Coutts. However, the use of generalized linear models in actuarial work is relatively new. Thus, McCullagh and Nelder give a number of examples of the fitting of generalized linear models to different types of data. One of these relates to data from Baxter et alS on the average claim costs in a motor insurance portfolio (originally modelled by Baxter et al. using a weighted least-squares approach). We made a small step in the direction of using generalized linear models in life insurance when we modelled the variation of lapse rates with age at entry, duration of policy, type of policy and insurance company''. Some of these models are described further in this paper. The purpose of the paper is to show that generalized linear models have a wide area of application in actuarial work and are not confined merely to models for motor insurance premiums. This purpose is fulfilled by demonstrating three separate practical applications in actuarial work: