Exact conditions for no ruin for the generalised Ornstein-Uhlenbeck   process
  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. 
Damien Bankovsky, Allan Sly