School Seminars and Colloquia

First passage problems for a Ornstein-Uhlenbeck process

Joint Seminar Series on Stochastic Processes and Financial Mathematics

by Alexander Novikov

Institution: Department of Mathematical Sciences, University of Technology, Sydney
Date: Thu 17th November 2005
Time: 1:15 PM
Location: Room 213, Richard Berry Building, The University of Melbourne

Abstract: The Ornstein-Uhlenbeck (O-U) processes with discrete and continuous
time parameter are used in engineering, statistical, actuarial and
financial applications. In this talk, we discuss several approaches
to boundary crossing problems for O-U processes. These include
integro-differential equations and martingale techniques. We find
some explicit formulas for the Laplace transform and expectation of
first passage times. As applications we consider the Exponentially
Weighted Moving Average (EWMA) procedure (used in statistical
quality control) and ruin probabilities under discrete and
continuous time settings.

For More Information: Prof Daniel Dufresne at, or Dr Aihua Xiaat