Finite time Parisian ruin of an integrated Gaussian risk model

In this paper we investigate the finite time Parisian ruin probability for an integrated Gaussian risk process. Under certain assumptions, we find that the Parisian ruin probability and the classical ruin probability are on the log-scale asymptotically the same. Moreover, if the time length required by the Parisian ruin tends to zero as the initial reserve goes to infinity, the Parisian ruin probability and the classical one are the same also in the precise asymptotic behavior. Furthermore, we derive an approximation for the scaled conditional ruin time.