A Class of Hierarchical Random Effect Models for Posterior Insurance Ratemaking

Abstract

Poisson random effect panel data model is widely used in non-life insurance for posterior rate making. Recently, Lee et al. (2020) identify one shortcoming of the shared random effect assumption, which introduces both the marginal count distribution and the serial dependence between counts at different periods. Therefore, it is not possible to accommodate separately these two features. This shortcoming also exists for any other nonlinear (say, gamma, or negative binomial) random effect regression model. In this note we propose a family of hierarchical random effect model, allowing to separate its effect on the marginal and the serial dependence structure of the observable dependent variables. The model we propose has several advantages. First it is very tractable, with closed form likelihood function and posterior rate making formula. Second, it is very general and suitable for a large number of marginal distributions of the random effect and conditional distributions of the response variable, such as the gamma-Poisson, beta-negative binomial pair distributions, as well as some new non conjugate pairs. Finally, it is also applicable to the simultaneous pricing of a large number of risks encountered in fleet insurance.