For a bivariate Lévy process (ξ
t
,η
t
)
t≥ 0 and initial value V
0 define the generalised Ornstein–Uhlenbeck (GOU) process V
t
:=eξ
t
(V
0+∫
t
0 e-ξ
s-
dη
s
), t≥0, and the associated stochastic integral process Z
t
:=∫0
t e-ξ
s-
dη
s
, t≥0. Let T
z
:=inf{t>0: V
t
<0|V
0=z} and ψ(z):=P(T
z
<∞) 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 T
z
as z→∞, under very general, easily checkable, assumptions, when ξ satisfies a Cramér condition.