Levy processes are a class of stochastic process which are useful in several areas of mathematics, especially insurance and financial mathematics. One area of specific interest is in functionals of the path of a Levy process, such as extrema, first passage time, and the last time an extrema was achieved. Wiener-Hopf factorization has proven to be a powerful tool in answering questions of this nature.

In this presentation, I will outline the general theory of Levy processes, and then describe Wiener-Hopf factorization theory in this context. I will give several examples, including the recent work by Alexey Kuznetsov in this area. An application to barrier option pricing will conclude the talk.