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Draw-down Parisian ruin for spectrally negative Lévy processes
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Draw-down Parisian ruin for spectrally negative Lévy processes
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Journal Article
Draw-down Parisian ruin for spectrally negative Lévy processes
2020
Overview
Draw-down time for a stochastic process is the first passage time of a draw-down level that depends on the previous maximum of the process. In this paper we study the draw-down-related Parisian ruin problem for spectrally negative Lévy risk processes. Intuitively, a draw-down Parisian ruin occurs when the surplus process has continuously stayed below the dynamic draw-down level for a fixed amount of time. We introduce the draw-down Parisian ruin time and solve the corresponding two-sided exit problems via excursion theory. We also find an expression for the potential measure for the process killed at the draw-down Parisian time. As applications, we obtain new results for spectrally negative Lévy risk processes with dividend barrier and with Parisian ruin.
Publisher
Cambridge University Press,Applied Probability Trust
Subject
