Exact conditions for no ruin for the generalised Ornstein-Uhlenbeck process

Damien Bankovsky, Allan Sly

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

For a bivariate Lévy process (ξt, ηt)t ≥ 0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as Vt {colon equals} eξt (z + ∫0t e- ξs - d ηs), t ≥ 0, where z ∈ R. We define necessary and sufficient conditions under which the infinite horizon ruin probability for the process is zero. These conditions are stated in terms of the canonical characteristics of the Lévy process and reveal the effect of the dependence relationship between ξ and η. We also present technical results which explain the structure of the lower bound of the GOU.

Original languageEnglish (US)
Pages (from-to)2544-2562
Number of pages19
JournalStochastic Processes and their Applications
Volume119
Issue number8
DOIs
StatePublished - Aug 1 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Exponential functionals of Lévy processes
  • Generalised Ornstein-Uhlenbeck process
  • Lévy processes
  • Ruin probability

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