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

Philip S. Griffin, Dale O. Roberts

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1331-1352
Number of pages22
JournalStochastic Processes and their Applications
Volume126
Issue number5
DOIs
StatePublished - 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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