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1 results

  • Draw-down Parisian ruin for spectrally negative Lévy processes

  • Part of
  • Wenyuan Wang, Xiaowen Zhou
  • Journal:
    Advances in Applied Probability / Volume 52 / Issue 4 / December 2020
    Published online by Cambridge University Press:
    03 December 2020, pp. 1164-1196
    Print publication:
    December 2020

  • 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.