Abstract

Let X be a jump diffusion, then its reflection at the boundaries 0 and b > 0 forms the process V . The amount by which V must reflect to stay within its boundaries is added to a process called the local time. This thesis establishes a large deviation principle for the local time of a reflected jump diffusion. Upon generalizing the notion of the local time to an additive functional, we establish the desired result through a Markov process argument. By applying Ito’s formula to a suitably chosen process M and in proving that M is a martingale, we find its associated integro-differential equation. M can then be used to find the limiting behavior of the cumulant generating function which allows the large deviation principle to be established by means of the Gartner-Ellis theorem. These theoretical results are then illustrated with two specific examples. We first find analytical results for these
examples and then test them in a Monte Carlo simulation study and by numerically solving the integro-differential equation.