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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 \(r\).

60G51 Processes with independent increments; Lévy processes
91B30 Risk theory, insurance (MSC2010)
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