Last exit before an exponential time for spectrally negative Lévy processes

Baurdoux, Erik J. ORCID: 0000-0002-5407-0683 (2009) Last exit before an exponential time for spectrally negative Lévy processes. Journal of Applied Probability, 46 (2). pp. 542-588. ISSN 0021-9002

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Abstract

In [5], the Laplace transform was found of the last time a spectrally negative Lévy process, which drifts to innity, is below some level. The main motivation for the study of this random time stems from risk theory: what is the last time the risk process, modeled by a spectrally negative Lévy process drifting to infinity, is zero? In this paper we extend the result found in [5] and we derive the Laplace transform of the last time before an independent, exponentially distributed time, that a spectrally negative Lévy process (without any further conditions) exceeds (upwards or downwards) or hits a certain level. As an application we extend a result found by Doney in [6].

Item Type:	Article
Official URL:	https://projecteuclid.org/euclid.jap
Additional Information:	© 2009 Applied Probability Trust
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	08 May 2009 10:27
Last Modified:	01 Oct 2024 03:35
URI:	http://eprints.lse.ac.uk/id/eprint/23924

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