On spectrally positive Lévy risk processes with Parisian implementation delays in dividend payments

In this note, we introduce a spectrally positive Lévy risk process with Parisian implementation delays in dividend payments, which means that the dividends can only be paid when the surplus of the Lévy risk process has stayed continuously above the barrier b for a certain time r(>0). Using the scale functions and the distribution of the risk process at time r, the Laplace transform of the ruin time is derived.