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

TL;DR

This paper derives explicit formulas for the distribution and Mellin transform of exponential functionals of Levy processes with rational Laplace exponents, extending previous work on hyper-exponential jump processes.

Contribution

It provides new explicit formulas for exponential functionals of Levy processes with rational jumps, broadening the class of processes with known distributions.

Findings

Explicit formulas for Mellin transforms derived

Distribution of exponential functionals characterized

Extension of previous hyper-exponential jump results

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)].