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.