Tail probabilities of subadditive functionals of Lévy processes

Michael Braverman, Thomas Mikosch, Gennady Samorodnitsky

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13 Scopus citations

Abstract

We study the tail behavior of the distribution of certain subadditive functional acting on the sample paths of Levy processes. The functional we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our results apply to ruin probabilities, distributions of sojourn times over curves, last hitting times and other functionals.

Original languageEnglish
Pages (from-to)69-100
Number of pages32
JournalAnnals of Applied Probability
Volume12
Issue number1
DOIs
StatePublished - 1 Feb 2002

Keywords

  • Heavy tails
  • Last hitting time
  • Lévy process
  • Negative drift
  • Risk
  • Ruin probability
  • Sojourn time
  • Subadditive functional
  • Supremum

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