Bankruptcy probabilities under non-Poisson inspection

This paper concerns an insurance firm’s surplus process observed at renewal inspection times, with a focus on assessing the probability of the surplus level dropping below zero. For various types of inter-inspection time distributions, an explicit expression for the corresponding transform is given. In addition, Cramér-Lundberg type asymptotics are established. Also, an importance sampling based Monte Carlo algorithm is proposed, and is shown to be logarithmically efficient.