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Some results about the expected ruin time in Markov-modulated risk models. (English) Zbl 0859.60081
Summary: We investigated the expected ruin time of Markov-modulated risk models. It turns out that the expected ruin time $$\xi(u)$$, depending on the initial risk reserve $$u\in\mathbb{R}^+$$, is asymptotically linear. In the two-state model we are able to derive exact formulas. A very interesting result is the monotonicity property of $$\xi(u)$$. We show that the more slowly the environment changes, the greater is the expected ruin time.

##### MSC:
 60K10 Applications of renewal theory (reliability, demand theory, etc.) 91B30 Risk theory, insurance (MSC2010)
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