Title: Derivation of killed processes: Applications in Finance

Abstract: 

In various fields including some in finance it is useful to have the concept of derivative of a killed process or a stopping time. We have started a project where such concepts can be discussed. Presently, we are developing some theoretical results that can be later applied. We will give a brief description of the project, achieved goals and some heuristics. I will present some results that have been obtained in joint work with Dan Crisan (Imperial College) in the one dimensional case and in the half space case. The generalizations of these results to the case of a smooth domain are being developed with Fabio Antonelli (University of L’Aquila). I will also briefly describe some possible financial applications.