On the dependence induced by frequency credibility models - 1 : Time-invariant random effects

In casualty insurance, actuaries usually resort to random effects to take unexplained heterogeneity into account in the spirit of the Bu ̈hlmann-Straub model. This paper aims to study the kind of dependence induced by the introduction of common latent variables in the annual numbers of claims reported by policyholders. It will be seen that this classical construction entails strong positive dependence between the underlying random variables