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Erlangian approximation to finite time ruin probabilities in perturbed risk models. (English) Zbl 1277.60128
Summary: In this paper, we consider a class of perturbed risk processes that have an underlying Markov structure, including Markov-modulated risk processes, and Sparre Andersen risk processes when both inter-claim times and claim sizes are phase-type. We apply the Erlangization method to the risk process in the class in order to obtain an accurate approximation of the finite time ruin probability. In addition, we develop an efficient recursive procedure by recognizing a repeating structure in the probability matrices we work with. We believe the present work is among the first to either compute or approximate finite time ruin probabilities in the perturbed risk model.

MSC:
60J28 Applications of continuous-time Markov processes on discrete state spaces
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60K05 Renewal theory
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