2000 character limit reached
Draw-down Parisian ruin for spectrally negative Lévy process (1904.03286v2)
Published 5 Apr 2019 in math.PR
Abstract: In this paper we study the draw-down related Parisian ruin problem for spectrally negative L\'{e}vy risk processes. We introduce the draw-down Parisian ruin time and solve the corresponding two-sided exit time via excursion theory. We also obtain an expression of the potential measure for the process killed at the draw-down Parisian time. As applications, new results are obtained for spectrally negative L\'{e}vy risk process with dividend barrier and Parisian ruin.