Maxima sampling on random time intervals for heavy-tailed compound renewal and Lévy processes
Seminar in Insurance and Economics
SPEAKER: Sergey Foss (Heriot-Watt University)
TITLE: Maxima sampling on random time intervals for heavy-tailed compound renewal and Lévy processes.
ABSTRACT: We derive the subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a Lévy process, both with negative drift, over random time horizon T that does not depend on the future increments of the process. Our asymptotic results are uniform over the whole class of such random times T. Particular examples are given by stopping times and by times independent of the processes. We link our results with the random walk theory. We also comment on a gap in the proof of one of results in the paper by Foss, Palmowski and Zachary (AnnAP, 2005). (Based on a joint work with Korshunov and Palmowski.)