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Parisian ruin probability for spectrally negative Lévy processes (1102.4055v2)
Published 20 Feb 2011 in math.PR, math.ST, q-fin.RM, and stat.TH
Abstract: In this note we give, for a spectrally negative Levy 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 Levy process and the distribution of the process at time r.