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Ruin theory for a Markov regime-switching model under a threshold dividend strategy. (English) Zbl 1141.91558
Summary: We study a Markov regime-switching risk model where dividends are paid out according to a certain threshold strategy depending on the underlying Markovian environment process. We are interested in these quantities: ruin probabilities, deficit at ruin and expected ruin time. To study them, we introduce functions involving the deficit at ruin and the indicator of the event that ruin occurs. We show that the above functions and the expectations of the time to ruin as functions of the initial capital satisfy systems of integro-differential equations. Closed form solutions are derived when the underlying Markovian environment process has only two states and the claim size distributions are exponential.

MSC:
91B30 Risk theory, insurance (MSC2010)
91B28 Finance etc. (MSC2000)
60G40 Stopping times; optimal stopping problems; gambling theory
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