Stochastics Seminar

Speaker: Dr. Jerzy Szulga

Abstract:Integrals of functions with respect to a stochastic process (a financial instrument) can be viewed as net financial gains under corresponding investments. A reasonable stochastic process (e.g., a Levy process) entails a natural (to be explained) metrizable topological space of integrands. For Brownian motion, it is just a Hilbert space and non-Gaussian stable processes yield L^p-spaces, p<2. In general, Levy process carry associated Orlicz spaces but they are not necessarily Banach (e.g., when the mean is infinite).

The lack of local convexity restricts the use of functionals yet there are ways around this obstacle.

We will show how the Levy measures determine such spaces, and how their properties (usually the type of growth) determine the properties of the underlying metric vector space, in particular, the local boundedness.