The expected value of the time of ruin and the moments of the discounted deficit at ruin in the perturbed classical risk process

In this paper, we consider the classical risk model that is perturbed by a Brownian motion process. We show that when claim sizes have a phase-type distribution, the probability of ruin, the Laplace transform of the time of ruin, the expected value of the time of ruin, the discounted moments of the deficit at ruin, and some other quantities of interests have explicit and easy to calculate formulas. Numerical examples are provided.