The uniform local asymptotics for a Lévy process and its overshoot and undershoot

Zhaolei Cui, Yuebao Wang and Kaiyong Wang

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 4, 1156-1181

Abstract: In this article, we obtain the uniform local asymptotics for a Lévy process with a heavy-tailed Lévy measure and for the overshoot and undershoot of the Lévy process. As applications, we get the uniform asymptotics of the finite-time ruin probability and the local ruin probability for the Lévy risk model with a heavy-tailed Lévy measure. By the above results, we find that in the compound Poisson model perturbed by a Brownian motion, the effect of the Brownian component on the asymptotics of the finite-time ruin probability and the local ruin probability washes out.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:45:y:2016:i:4:p:1156-1181

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DOI: 10.1080/03610926.2013.861492

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