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Parisian ruin probability for spectrally negative Lévy processes. (English) Zbl 1267.60054
Summary: We give, for a spectrally negative Lévy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period $$r$$. The formula involves only the scale function of the spectrally negative Lévy process and the distribution of the process at time $$r$$.

##### MSC:
 60G51 Processes with independent increments; Lévy processes 91B30 Risk theory, insurance (MSC2010)
##### Keywords:
Lévy process; Parisian ruin; risk process; ruin probability
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##### References:
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