Pricing Automobile Insurance under Multivariate Classification of Risks: Additive versus Multiplicative

For most auto insurance coverages, insureds are cross-classified by at least two variables: driver class and territory. Traditional classification rate-making has employed a multiplicative technique equivalent to the assumption of a completely interactive model. In this paper, the traditional method and the closely associated log-linear model are found, for recent Massachusetts experience, to lead to biased pricing for drivers in high-rate class-territory combinations. An additive model eliminates this bias and has slightly superior overall accuracy. Constraints are selected so that model parameters describe natural actuarial quantities. The different effects of dependency in exposure distributions and interaction between variables are brought into focus.