Some results about the expected ruin time in Markov-modulated risk models

In this paper we investigate the expected ruin time of Markov-modulated risk models. It turns out that the expected ruin time ξ(u), depending on the initial risk reserve u ∈ R+, is asymptotically linear. In the two-state model we are able to derive exact formulas. A very interesting result is the monotonicity property of ξ(u). We show that the more slowly the environment changes, the greater is the expected ruin time.