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

Philip S. Griffin; Dale O. Roberts

doi:10.1016/j.spa.2015.11.005

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

Philip S. Griffin, Dale O. Roberts

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let X be a Lévy process and τ(u)=inf{t:X_t>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.

Original language	English (US)
Pages (from-to)	1331-1352
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	126
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2015.11.005
State	Published - May 2016

Keywords

Asymptotic
Convolution equivalent
First passage within finite time
Insurance risk
Lévy processes
Semi-heavy tails
Subexponential

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/j.spa.2015.11.005

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abstract = "Let X be a L{\'e}vy 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)",

keywords = "Asymptotic, Convolution equivalent, First passage within finite time, Insurance risk, L{\'e}vy processes, Semi-heavy tails, Subexponential",

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AU - Roberts, Dale O.

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KW - First passage within finite time

KW - Insurance risk

KW - Lévy processes

KW - Semi-heavy tails

KW - Subexponential

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

Abstract

Keywords

ASJC Scopus subject areas

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