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Last exit before an exponential time for spectrally negative Lévy processes

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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].

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en

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application/pdf

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http://eprints.lse.ac.uk/23924/1/Last_exit_before_an_exponential_time_for_spectrally_negative_L%C3%A9vy_processes_%28lsero%29.pdf

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