Thursday, October 1, 2009
10:30 AM in LWSN 1142
Ionut Florescu
Department of Mathematical Sciences, Stevens Institute of Technology

A study of an integro-differential parabolic problem arising in Mathematics of Finance

Abstract

In Finance one of the most studied problems is pricing options when the underlying equity follows a stochastic process. If the underlying process is a regular diffusion the problem is reduced to solving a Partial Differential Equation. However, if the underlying process possesses jumps (or more general a Lévy component) an integral term arises in the defining equation due to the associated Levy measure. This produces the so called Partial Integro-Differential Equations. Problems of existence, uniqueness and determination of solutions for such equations are still open. In this talk I will present a proof of existence on general domains under suitable conditions on the integral operator. The proof is based on the method of upper and lower solutions and also provides an algorithm to approximate the solution. The work is based on the collaboration with Prof. Maria C. Mariani from University of Texas at El Paso