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On the discounted penalty function in a Markov-dependent risk model. (English) Zbl 1129.91023
Summary: We present a unified approach to the analysis of several popular models in collective risk theory. Based on the analysis of the discounted penalty function in a semi-Markovian risk model by means of Laplace-Stieltjes transforms, we rederive and extend some recent results in the field. In particular, the classical compound Poisson model, Sparre Andersen models with phase-type interclaim times and models with causal dependence of a certain Markovian type between claim sizes and interclaim times are contained as special cases.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K15 Markov renewal processes, semi-Markov processes
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
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