We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Lévy processes with rational Laplace exponent. This extends recent results by Cai and Kou [3] on the processes with hyper-exponential jumps.

We study the density of the supremum of a strictly stable Lévy process. Our first goal is to investigate convergence properties of the series representation for this density, which was established recently by Hubalek and Kuznetsov (2011) [24]. Our second goal is to investigate in more detail...