Ratemaking: from Bailey and Simon (1960) to Generalised Linear Regression Models

ABSTUACT The Bailey and Simon (1960) and Bailey (1963) papers on class and merit rating discuss models and estimation criteria in a non-probabilistic framework. lt has been shown, for example, Van Eeghen et al (1983), that the Bailey and Simon criterion of class balance is equivalent to maximum likelihood estimation of a claim frequency modal with Poisson distributed ctajm numbers. It tums out that the Poisson based model is part of a large body of recently developed statistical methodology known as Generalised Linear Regression fvlodelling. Indeed, the Bailey and Simon papers provide the motivation for generalised linear regression models. By applying the regression framework some results are developed that relate the various estimation criteria and a number of extensions are given for the case where the condition of class balance is not appropriate as a result of lack of credibility for some of the classes. The regression framework moreover facilitates the consideration of a much wider family of models than that considered by Bailey and Simon. Generalised regression models are also motivated and indeed introduced as an extension to the classical normal based regression models. Many of the benefits afforded by regression modelling are discussed.