  Let $\{B(t), t\ge 0\}$ be a Brownian motion. Consider the Brownian motion
risk model with interest rate collection and tax payment defined by
\begin{align}\label{Rudef}
\widetilde{U}_\gamma^\delta(t)=\widetilde{X}^\delta(t)-\gamma\sup_{s\in[0,t]}
\left(\widetilde{X}^\delta(s)e^{\delta(t-s)}-ue^{\delta(t-s)}\right),t\ge0,
\end{align} with $$\widetilde{X}^\delta(t)=ue^{\delta t}+c \int_0^t e^{\delta
(t-v)}dv-\sigma \int_0^t e^{\delta(t-v)}dB(v),$$ where $c>0,\gamma \in [0,1)$
and $\delta \in \mathbb{R}$ are three given constants. When $\delta=0$ and
$\gamma \in (0,1)$ this is the risk model introduced from Albrecher and Hipp in
\cite{AH2007} where the ruin probability in the infinite time horizon has been
explicitly calculated. In the presence of interest rate $\delta\neq0$, the
calculation of ruin probability for this risk process for both finite and
infinite time horizon seems impossible. In the paper, based on asymptotic
theory we propose an approximation for ruin probability and ruin time when the
initial capital $u$ tends to infinity. Our results are of interest given the
fact that this can be used as benchmark model in various calculations.
