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Some ruin problems for the MAP risk model. (English) Zbl 1348.91163
Summary: We consider ruin problems for a risk model with a Markovian arrival process (MAP). In particular, we study (1) the density of the time of ruin under two different assumptions on the premium income, by using two approaches; (2) the probability function of the number of claims until the time of ruin; (3) the moments of the time of ruin by developing a recursive approach.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K25 Queueing theory (aspects of probability theory)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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