  The collective risk model (CRM) for frequency and severity is an important
tool for retail insurance ratemaking, macro-level catastrophic risk
forecasting, as well as operational risk in banking regulation. This model,
which is initially designed for cross-sectional data, has recently been adapted
to a longitudinal context to conduct both a priori and a posteriori ratemaking,
through the introduction of random effects. However, so far, the random
effect(s) is usually assumed static due to computational concerns, leading to
predictive premium that omit the seniority of the claims. In this paper, we
propose a new CRM model with bivariate dynamic random effect process. The model
is based on Bayesian state-space models. It is associated with the simple
predictive mean and closed form expression for the likelihood function, while
also allowing for the dependence between the frequency and severity components.
Real data application to auto insurance is proposed to show the performance of
our method.
