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Last exit before an exponential time for spectrally negative Lévy processes

Baurdoux, Erik J. (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
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Risk and Stochastics Group
Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 08 May 2009 10:27
URL: http://eprints.lse.ac.uk/23924/

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