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 language | English (US) |
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Pages (from-to) | 712-734 |
Number of pages | 23 |
Journal | Advances in Applied Probability |
Volume | 43 |
Issue number | 3 |
DOIs | |
State | Published - Sep 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