On the distribution of exponential functionals for Levy processes with jumps of rational transform

Abstract

We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou on the processes with hyper-exponential jumps [N. Cai and S. Kou "Prising Asian options under a general jump diffusion model", (2010)].