A m-type risk model with Markov-modulated premium rate

In this paper, we consider a m-type risk model with Markovmodulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the Kn-family, n ∈ N+. One example is given with claim sizes that have exponential distributions.