Applications of factorization embeddings for Lévy processes
- 1 September 2006
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 38 (3), 768-791
- https://doi.org/10.1239/aap/1158685001
Abstract
We give three applications of the Pecherskii-Rogozin-Spitzer identity for Lévy processes. First, we find the joint distribution of the supremum and the epoch at which it is ‘attained’ if a Lévy process has phase-type upward jumps. We also find the characteristics of the ladder process. Second, we establish general properties of perturbed risk models, and obtain explicit fluctuation identities in the case that the Lévy process is spectrally positive. Third, we study the tail asymptotics for the supremum of a Lévy process under different assumptions on the tail of the Lévy measure.Keywords
This publication has 26 references indexed in Scilit:
- On Maxima and Ladder Processes for a Dense Class of Lévy ProcessJournal of Applied Probability, 2006
- Tail asymptotics for exponential functionals of Lévy processesStochastic Processes and their Applications, 2006
- Overshoots and undershoots of Lévy processesThe Annals of Applied Probability, 2006
- Ruin probabilities and overshoots for general Lévy insurance risk processesThe Annals of Applied Probability, 2004
- Ruin probabilities and decompositions for general perturbed risk processesThe Annals of Applied Probability, 2004
- Stochastic bounds for Lévy processesThe Annals of Probability, 2004
- Distribution of the first ladder height of a stationary risk process perturbed by α-stable Lévy motionInsurance: Mathematics and Economics, 2001
- Risk processes perturbed by α-stable Lévy motionScandinavian Actuarial Journal, 1998
- On distribution tail of the maximum of a random walkStochastic Processes and their Applications, 1997
- Extreme Values in the GI/G/1 QueueThe Annals of Mathematical Statistics, 1972