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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.

91B30 Risk theory, insurance (MSC2010)
Full Text: DOI
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