  Let $B(t), t\in \mathbb{R}$ be a standard Brownian motion. Define a risk
process \label{Rudef} R_u^{\delta}(t)=e^{\delta
t}\left(u+c\int^{t}_{0}e^{-\delta s}d s-\sigma\int_{0}^{t}e^{-\delta s}d
B(s)\right), t\geq0, where $u\geq 0$ is the initial reserve, $\delta\geq0$ is
the force of interest, $c>0$ is the rate of premium and $\sigma>0$ is a
volatility factor. In this contribution we obtain an approximation of the
Parisian ruin probability
\mathcal{K}_S^{\delta}(u,T_u):=\mathbb{P}\left\{\inf_{t\in[0,S]}
\sup_{s\in[t,t+T_u]} R_u^{\delta}(s)<0\right\}, S\ge 0, as $u\rightarrow\infty$
where $T_u$ is a bounded function. Further, we show that the Parisian ruin time
of this risk process can be approximated by an exponential random variable. Our
results are new even for the classical ruin probability and ruin time which
correspond to $T_u\equiv0$ in the Parisian setting.
