AbstractsMathematics

The Levy Khintchine formula plays a central role in the theory of Levy processes. But, the full extension of this formula on a manifold is, to date, not known. We will be studying this problem from the perspective of a symmetric space. The Levy Khintchine formula on a symmetric space, for a special class of Levy processes (Isotropic processes), was first obtained by Gangolli in 1964. Since then, no significant progress was made for general Levy processes on a symmetric space. This thesis derives the Levy Khintchine formula on a symmetric space for a general Levy process, and then explores a possible application to the pricing of financial derivatives.