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

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

2008-04-10

arxiv.org/abs/0804.1634v1

Mathematics

Probability

24 pages

Scientific paper

For a bivariate L\'evy process $(\xi_t,\eta_t)_{t\geq 0}$ the generalised Ornstein-Uhlenbeck (GOU) process is defined as V_t:=e^{\xi_t}(z+\int_0^t e^{-\xi_{s-}}d\eta_s), t\ge0, where $z\in\mathbb{R}.$ 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 L\'evy process and reveal the effect of the dependence relationship between $\xi$ and $\eta.$ We also present technical results which explain the structure of the lower bound of the GOU.

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