Stability of the exit time for Lévy processes

Philip S. Griffin, Ross A. Maller

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

This paper is concerned with the behaviour of a Lévy process when it crosses over a positive level, u, starting from 0, both as u becomes large and as u becomes small. Our main focus is on the time, τu, it takes the process to transit above the level, and in particular, on the stability of this passage time; thus, essentially, whether or not τu behaves linearly as u → 0 or u→∞. We also consider the conditional stability of tu when the process drifts to -∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cramér condition.

Original languageEnglish (US)
Pages (from-to)712-734
Number of pages23
JournalAdvances in Applied Probability
Volume43
Issue number3
DOIs
StatePublished - Sep 1 2011

Keywords

  • Cramér condition
  • Insurance risk process
  • Lévy process
  • Overshoot
  • Passage time above a level
  • Stability

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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