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Sample paths of a Lévy process leading to first passage over high levels in finite time

Sample paths of a Lévy process leading to first passage

Philip Griffin and Dale Roberts

Let X be a Lévy process and τ(u)=inf{t:Xt>u} the first passage time of X over level u. For fixed T˂∞ sharp asymptotic estimates for P(τ(u)<T) as u→∞ have been developed for several classes of Lévy processes.

In this paper we investigate the asymptotic behavior of the sample paths of the process which lead to first passage by time T. This complements previous work in the T˂∞ case and is motivated, in part, by problems in insurance risk.

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Updated:   18 February 2017 / Responsible Officer:  CBE Communications and Outreach / Page Contact:  College Web Team