Ruin Problems for Risk Processes with Dependent Phase-Type Claims

We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the dependence between claims in a simple and intuitive way. It is also designed to facilitate the study of the risk processes by using a Markov-modulated fluid embedding technique. Using this technique, we obtain simple recursive procedures to determine the joint distribution of the time of ruin, the deficit at ruin and the number of claims before the ruin. We also obtain some bounds for the ultimate ruin probability. Finally, we provide a few examples of multivariate phase-type distributions and use them for numerical illustration.