Abstract

Meromorphic L´evy processes have attracted the attention of a lot of researchers recently
due to its special structure of the Wiener-Hopf factors as rational functions of infinite degree
written in terms of poles and roots of the Laplace exponent, all of which are real numbers.
With these Wiener-Hopf factors in hand, we can explicitly derive the expression of fluctuation
identities that concern the first passage problems for finite and infinite intervals for
the meromorphic L´evy process and the resulting process reflected at its infimum. In this
thesis, we consider some fluctuation identities of some classes of meromorphic jump-diffusion
processes with either the double exponential jumps or more general the hyper-exponential
jumps. We study solutions to the one-sided and two-sided exit problems, and potential measure
of the process killed on exiting a finite or infinite intervals. Also, we obtain some results
to the process reflected at its infimum.