Risk Processes with Interest Force in Markovian Environment

Abstract

We consider risk processes modulated by an external Markov chain, with claim amounts following phase-type distributions, featuring an interest rate factor. We are interested in the distribution of exit times, which we study through proper transformations of the original processes, through duality and Markovian embeddings. In dimension 1, this corresponds to the classic ruin time of which we compute the distribution. We also consider K dimensional processes, of which exits out of quadrants are studied.