On suprema of Lévy processes and application in risk theory

Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review

Abstract

Let X̂ = C - Y where Y is a general one-dimensional Lévy process and C an independent subordinator. Consider the times when a new supremum of X̂ is reached by a jump of the subordinator C. We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and X drifts to -oo, we decompose the absolute supremum of X̂ at these times, and derive a Pollaczek-Hinchin-type formula for the distribution function of the supremum.

Original languageEnglish (US)
Pages (from-to)977-986
Number of pages10
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume44
Issue number5
DOIs
StatePublished - Oct 2008

Keywords

  • Extrema
  • Fluctuation theory
  • Lévy process
  • Risk theory
  • Subordinator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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