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On the analysis of a multi-threshold Markovian risk model. (English) Zbl 1164.91025
This paper deals with a class of Markovian risk models perturbed by a multiple threshold dividend strategy in which the insurer collects premiums at rate \(c_{i}\) whenever the surplus level resides in the \(i\)-th surplus layer, \(i=1,2,\dots,n+1\) where \(n<\infty\). The Laplace-Stieltjes transform of the distribution of the time to ruin is derived as well as the discounted joint density of the surplus prior to ruin and the deficit at ruin. In the case, when the insurer, whose gross premium rate is \(c\), pays dividends continuously at rate \(c-c_{i}\) whenever the surplus level resides in the \(i\)-th surplus layer, the authors derive the expected discounted value of total dividend payments made prior to ruin.

MSC:
91B30 Risk theory, insurance (MSC2010)
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