BAYESIAN ANALYSIS OF THE COMPOUND COLLECTIVE MODEL: THE NET PREMIUM PRINCIPLE WITH EXPONENTIAL POISSON AND GAMMA–GAMMA DISTRIBUTIONS

This article develops a Bayesian analysis of the Compound Collective Model utilizing the Net Premium Principle, considering single-period models. With respect to likelihoods, we used a Poisson distribution for the number of claims and an Exponential distribution for the severity of the accident/event. Gamma distributions were used for the prior distributions. The robustness of the posterior premium was analyzed with respect to the prior distribution specification of the severity of the accident/event, utilizing contamination classes, these being the class of all the distributions and that of all the unimodal distributions with the same mode. Numerical applications of the results obtained were performed.