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The expected time to ruin in a risk process with constant barrier via martingales. (English) Zbl 1117.91381
Summary: Two risk models with a constant dividend barrier are considered. In the two models claims arrive according to a Poisson process. In the first model the claim size has a phase type distribution. In the second model the claim size is exponentially distributed, but the arrival rate, the mean claim size, and the premium rate are governed by a random environment, which changes according to a Markov process. O. Kella and W. Whitt [J. Appl. Probab. 29, 396–403 (1992; Zbl 0761.60065)] martingale is applied in the first model. S. Asmussen and S. Kella [Adv. Appl. Probab. 32, 376–393 (2000; Zbl 0961.60081)] multi-dimensional martingale is applied in the second model. The expected time to ruin and the amount of dividends paid until ruin occurs are obtained for both models.

##### MSC:
 91B30 Risk theory, insurance (MSC2010)
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##### References:
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