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We consider continuous time risk processes in which the claim sizes aredependent and non-identically distributed phase-type distributions. The classof distributions we propose is easy to characterize and allows to incorporatethe dependence between claims in a simple and intuitive way. It is alsodesigned to facilitate the study of the risk processes by using aMarkov-modulated fluid embedding technique. Using this technique, we obtainsimple recursive procedures to determine the joint distribution of the time ofruin, the deficit at ruin and the number of claims before the ruin. We alsoobtain some bounds for the ultimate ruin probability. Finally, we provide a fewexamples of multivariate phase-type distributions and use them for numericalillustration.

Ruin problems for risk processes with dependent phase-type claims