g/m/1 type structure in a regime-switching risk model with general claim sizes
We consider a discrete time regime-switching risk model, where the claim occurrence probabilities and the claim size distributions depend on the regime of the environment. We assume that the regime is governed by a Markov process with a finite state space and the claim sizes have general distributions. We observe a G/M/1 type structure in the process of the surplus level and the regime, and employ the matrix analytic method to analyze the sojourn time of the surplus process at each level until the ruin time. Using the results on the surplus process at each level until the ruin time, we derived the the ruin probability. Numerical examples are provided to show the validity of the numeric computations.
risk model surplus process ruin probability first passage time