TY - JOUR
T1 - Stability of the exit time for Lévy processes
AU - Griffin, Philip S.
AU - Maller, Ross A.
PY - 2011/9
Y1 - 2011/9
N2 - 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.
AB - 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.
KW - Cramér condition
KW - Insurance risk process
KW - Lévy process
KW - Overshoot
KW - Passage time above a level
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=80053401158&partnerID=8YFLogxK
U2 - 10.1239/aap/1316792667
DO - 10.1239/aap/1316792667
M3 - Article
SN - 0001-8678
VL - 43
SP - 712
EP - 734
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 3
ER -