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Dependent risk models with bivariate phase-type distributions. (English) Zbl 1172.91009

The paper investigates an extension of the Sparre Andersen insurance risk model. More precisely, the joint distribution of the interclaim time and the subsequent claim size is bivariate phase-type (the model permits the dependence between the claim size and interclaim time). The analysis of certain characteristics of the risk process predicates on the connection between surplus processes and fluid queues. The Laplace transform of the time to ruin is derived. As a corollary the infinite time ruin probability, the deficite at ruin and the Gerber–Shiu function are given. Finally, the surplus prior to ruin is investigated.

MSC:

91B30 Risk theory, insurance (MSC2010)
60J25 Continuous-time Markov processes on general state spaces
60J75 Jump processes (MSC2010)
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