Let
B(t),t∈R be a standard Brownian motion. Define a risk process
where
3e01a8b3a01" title="Click to view the MathML source">u≥0 is the initial reserve,
03036eb638c38699982aa87232aa2504" title="Click to view the MathML source">δ≥0 is the force of interest,
0391f" title="Click to view the MathML source">c>0 is the rate of premium and
032bc373e3535f348c" title="Click to view the MathML source">σ>0 is a volatility factor. In this contribution we obtain an approximation of the Parisian ruin probability
as
u→∞ where
Tu 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
03117b781a" title="Click to view the MathML source">Tu≡0 in the Parisian setting.