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Discrete time ruin probability with Parisian delay. (English) Zbl 1402.91188
Summary: In this paper we evaluate the probability of the discrete time Parisian ruin that occurs when surplus process stays below or at zero at least for some fixed duration of time \(d>0\). We identify expressions for the ruin probabilities within finite and infinite-time horizon. We also find their light and heavy-tailed asymptotics when initial reserves approach infinity. Finally, we calculate these probabilities for a few explicit examples.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60G51 Processes with independent increments; Lévy processes
62P05 Applications of statistics to actuarial sciences and financial mathematics
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