機率研討會
主講者: | Prof. Steven Kou (National University of Singapore) |
講題: | First Passage Times of Two-Dimensional Brownian Motion |
時間: | 2013-08-19 (Mon.) 14:10 - 15:10 |
地點: | 數學所 722 研討室 (台大院區) |
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. |
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