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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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##### References:
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