Finite time ruin problems for the Markov-modulated risk model

We consider finite time ruin problems in the Markov-modulated risk model. We start by considering the number of claims and the aggregate claim amount over a finite time interval, in each case giving both a general approach for an arbitrary number of environment states and a specific approach for the special case when the number of environment states is two. We then consider the density of the time of ruin and the joint density of the time of ruin and the deficit at ruin, before developing a recursive approach to the calculation of the moments of the time of ruin. We conclude with a study of some discrete random variables associated with a Markov-modulated risk model. Numerical illustrations are provided.