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Distributions of the surplus before ruin, the deficit at ruin and the claim causing ruin in a class of discrete time risk models. (English) Zbl 1143.91033
The author considers extensions of the compound binomial risk model in a class of discrete time Sparre Andersen risk models in which probability generating function (p.g.f.) of the claim inter- arrival times distribution function is a ratio of two polynomials of order \(m\in N^+\). He shows that the Gerber-Shiu function can be expressed explicitly in terms of a compound geometric distribution function which has closed expressions other than convolution forms for two classes of claim size distributions. It is also shown that 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 can be obtained with the help of appropriately chosen penalty function.

MSC:
91B30 Risk theory, insurance (MSC2010)
60G40 Stopping times; optimal stopping problems; gambling theory
60K15 Markov renewal processes, semi-Markov processes
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