  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, Cram\'er-Lundberg type asymptotics are established. Also, an
importance sampling based Monte Carlo algorithm is proposed, and is shown to be
logarithmically efficient.
