Ruin probabilities for a regenerative Poisson gap generated risk process

A risk process with constant premium rate c and Poisson arrivals of claims is considered. A threshold r is defined for claim interarrival times, such that if k consecutive interarrival times are larger than r, then the next claim has distribution G. Otherwise, the claim size distribution is F . Asymptotic expressions for the infinite horizon ruin probabilities are given for both lightand the heavy-tailed cases. A basic observation is that the process regenerates at each G-claim. Also an approach via Markov additive processes is outlined, and heuristics are given for the distribution of the time to ruin.