On ruin probability for a risk process perturbed by a levy process with no negative jumps

We study a risk process where the claim sizes and the interarrival times are phase-type distributed. The risk process is perturbed by a Levy process with no negative jumps. We derive the ruin probability, and the distribution of deficit at ruin, by constructing an unperturbed risk process with the same ruin probability. In this process, the claim sizes are also phase-type, and the interarrival times have some general distribution. The interarrival times and the claims are dependent. The model is analyzed via the dual queueing system, which we show to be of the Markov arrival process type.