Author:
Bankovsky Damien,Klüppelberg Claudia,Maller Ross
Abstract
For a bivariate Lévy process (ξt,ηt)t≥ 0and initial valueV0define the generalised Ornstein–Uhlenbeck (GOU) processVt:=eξt(V0+∫t0e-ξs-dηs),t≥0, and the associated stochastic integral processZt:=∫0te-ξs-dηs,t≥0. LetTz:=inf{t>0:Vt<0|V0=z} and ψ(z):=P(Tz<∞) forz≥0 be the ruin time and infinite horizon ruin probability of the GOU process. Our results extend previous work of Nyrhinen (2001) and others to give asymptotic estimates for ψ(z) and the distribution ofTzasz→∞, under very general, easily checkable, assumptions, when ξ satisfies a Cramér condition.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
4 articles.
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