On moments of downward passage times for spectrally negative Lévy processes

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Abstract

The existence of moments of first downward passage times of a spectrally negative Lévy process is governed by the general dynamics of the Lévy process, i.e. whether it is drifting to, or oscillating. Whenever the Lévy process drifts to, we prove that the th moment of the first passage time (conditioned to be finite) exists if and only if the th moment of the Lévy jump measure exists. This generalizes a result shown earlier by Delbaen for Cramér-Lundberg risk processes. Whenever the Lévy process drifts to, we prove that all moments of the first passage time exist, while for an oscillating Lévy process we derive conditions for non-existence of the moments, and in particular we show that no integer moments exist.

Details

OriginalspracheEnglisch
Seiten (von - bis)452-464
Seitenumfang13
FachzeitschriftJournal of Applied Probability
Jahrgang60
Ausgabenummer2
PublikationsstatusVeröffentlicht - 2023
Peer-Review-StatusJa

Externe IDs

Scopus 85159311158
ORCID /0000-0002-9999-7589/work/142238030

Schlagworte

Schlagwörter

  • Conjugate subordinator, Cramér-Lundberg risk process, exit time, first hitting time, fluctuation theory, fractional calculus, moments, ruin theory, spectrally negative Lévy process, subordinator, time to ruin

Bibliotheksschlagworte