Abstract
AbstractThe 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
$+\infty$
,
$-\infty$
, or oscillating. Whenever the Lévy process drifts to
$+\infty$
, we prove that the
$\kappa$
th moment of the first passage time (conditioned to be finite) exists if and only if the
$(\kappa+1)$
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
$-\infty$
, 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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
1 articles.
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1. Moments of the Ruin Time in a Lévy Risk Model;Methodology and Computing in Applied Probability;2022-07-30