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Draw-down Parisian ruin for spectrally negative L\'{e}vy process. (arXiv:1904.03286v2 [math.PR] UPDATED)

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.查看全文

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