Ultimate ruin probability in discrete time with Bühlmann credibility premium adjustments

In this paper, we consider a discrete-time ruin model where experience rating is taken into account. The main objective is to determine the behavior of the ultimate ruin probabilities for large initial capital in the case of light-tailed claim amounts. The logarithmic asymptotic behavior of the ultimate ruin probability is derived. Typical pathes leading to ruin are studied. An upper bound is derived on the ultimate ruin probability in some particular case. The influence of the number of data points taken into account is analyzed, and numerical illustrations support the theoretical findings. Finally, we investigate the heavy-tailed case. The impact of the number of data points used for the premium calculation appears to be rather different from the one in the light-tailed case.