Ruin probabilities for Bayesian exchangeable claims processes

Among the driving assumptions in classical collective risk models, the independence among claims is frequently violated by real applications. Therefore, there is an evident need of models that relax such a restriction. We undertake the exchangeable claims platform and obtain some results for the infinite time ruin probability. The main result is that the ruin probability under the exchangeable claims model can be represented as the expected value of the ruin probabilities corresponding to certain independent claims cases. This allows us to extend some classical results to this dependent claims scenario. The main tool is based on the de Finetti’s representation theorem for exchangeable random variables, and as a consequence a natural Bayesian modeling feature for risk processes becomes available. In particular, an interesting redefinition of the net profit condition is necessary.