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On a classical risk model with a constant dividend barrier. (English) Zbl 1215.60051
Summary: This paper considers a risk model with a constant dividend barrier. It first points out interesting connections between some previous results for this model and those for spectrally negative Levy processes. An expression is then obtained for the joint distribution of the surplus immediately prior to ruin and the deficit at ruin, discounted from the time of ruin. Such an expression involves known results on the joint distribution at ruin for a classical risk model without barrier. Also discussed are the joint distributions related to the time periods when dividends are paid. In particular, this paper obtains the Laplace transform for the total dividend payments until ruin, and another expression for the expected present value of the total amount of dividend payments until ruin. The results do not require the positive loading condition.

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K05 Renewal theory
91B30 Risk theory, insurance (MSC2010)
Keywords:
ruin; risk; model; Laplace
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