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On a class of discrete time renewal risk models. (English) Zbl 1142.91043
The paper explores extensions of the compound binomial risk model in a class of discrete time Sparre Andersen risk models. It is shown that in this class of compound renewal risk process, which claim size distributions have a rational or polynomial probability generating function (p.g.f.), the defective probability can be obtained explicitly. Using such tool of generating functions, a recursive formula for the expected discounted penalty (Gerber-Shiu) function is derived, which then can be used to obtain explicit expressions for the p.g.f. of the time ruin, the joint and marginal distributions of the surplus before ruin, the deficit at ruin, the claim causing ruin, as well as their moments.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K15 Markov renewal processes, semi-Markov processes
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