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For a bivariate \Levy process $(\xi_t,\eta_t)_{t\geq 0}$ the generalisedOrnstein-Uhlenbeck (GOU) process is defined as \[V_t:=e^{\xi_t}(z+\int_0^te^{-\xi_{s-}}\ud \eta_s), t\ge0,\]where $z\in\mathbb{R}.$ We present conditionson the characteristic triplet of $(\xi,\eta)$ which ensure certain ruin for theGOU. We present a detailed analysis on the structure of the upper and lowerbounds and the sets of values on which the GOU is almost surely increasing, ordecreasing. This paper is the sequel to \cite{BankovskySly08}, which statedconditions for zero probability of ruin, and completes a significant aspect ofthe study of the GOU.

Conditions for certain ruin for the generalised Ornstein-Uhlenbeck process and the structure of the upper and lower bounds