Speaker :
| Prof. Steven Kou (National University of Singapore) |
Title :
|
First Passage Times of Two-Dimensional Brownian Motion |
Time :
| 2013-08-19 (Mon) 14:10 - |
Place : |
Seminar Room 722, Institute of Mathematics (NTU Campus) |
Abstract: |
First passage times of two-dimensional Brownian motion have been used to study correlated defaults under structural models in finance. However, despite various attempts since 1950's, there are few analytical solutions available. By analytically solving a modified Helmholtz equation in an infinite wedge with non-homogenous boundary conditions, we propose a unified approach to obtain analytical solutions to these problems. We also point out a link between the Laplace transforms of the first passage times and a bivariate exponential distribution which is absolute continuous but does not have memoryless property.
This is a joint work with Haowen Zhong. |