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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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