On moments of downward passage times for spectrally negative Lévy processes

Research output: Contribution to journalResearch articleContributedpeer-review


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.


Original languageEnglish
Pages (from-to)452-464
Number of pages13
JournalJournal of Applied Probability
Issue number2
Publication statusPublished - 2023

External IDs

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



  • 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

Library keywords