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On the ruin probability of the generalised Ornstein–Uhlenbeck process in the cramér case
Published online by Cambridge University Press: 14 July 2016
Abstract
For a bivariate Lévy process (ξt,ηt)t≥ 0 and initial value V0 define the generalised Ornstein–Uhlenbeck (GOU) process Vt:=eξt (V0+∫t0 e-ξs-dηs), t≥0, and the associated stochastic integral process Zt:=∫0t e-ξs-dηs, t≥0. Let Tz:=inf{t>0: Vt<0|V0=z} and ψ(z):=P(Tz<∞) for z≥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 of Tz as z→∞, under very general, easily checkable, assumptions, when ξ satisfies a Cramér condition.
Keywords
- Type
- Part 1. Risk Theory
- Information
- Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 15 - 28
- Copyright
- Copyright © Applied Probability Trust 2011
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