This paper revisits the spectrally negative Lévy risk process embedded with the general tax structure introduced in Kyprianou and Zhou (2009). A joint Laplace transform is found concerning the first down-crossing time below level 0. The potential density is also obtained for the taxed Lévy risk...

Using a Poisson approach, we find Laplace transforms of joint occupation times over n disjoint intervals for spectrally negative Lévy processes. They generalize previous results for dimension two.