On the stochastic increasingness of future claims in the Bühlmann linear credibility premium

Since Nelder & Verrall (1997), the connection between Generalized Linear Mod- els (GLM’s) and credibility theory has been recognized in actuarial science. Specifically, the credibility construction amounts to add a random effect on the same scale as the fixed effects to model unexplained heterogeneity. The present paper aims to examine the dependence ex- isting between future claims (severity or frequency components) and the Bu ̈hlmann linear credibility premium. As expected, future claims are shown to increase with the amount of Bu ̈hlmann premium