Parisian ruin probability for spectrally negative L\'{e}vy processes
  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. 
Ronnie Loeffen, Irmina Czarna, Zbigniew Palmowski
math.PR math.ST q-fin.RM stat.TH