Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon

Abstract

Let be a standard Brownian motion. In this paper, we derive the asymptotics of the probability of Parisian ruin over an infinite time horizon for the following risk process (0.1) where is the initial reserve, is the force of interest, is the rate of premium and is a volatility factor. It turns out that the Parisian ruin probability decays exponentially as u tends to infinity and is a decreasing function of the force of interest for u large. Moreover, we obtain the approximations of Parisian ruin time.