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      Department of Systems Engineering and Engineering Management

                             The Chinese University of Hong Kong

 

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Title: First Passage Times of Two-Dimensional Brownian Motion.

 

 

Speaker: Steven KOU, National University of Singapore 

 

 

Abstract: 

First passage times (FPTs) of two-dimensional Brownian motion have seen numerous applications in quantitative finance, such as in studying default correlations under structural models of credit risk, among others. However, despite various attempts since the 1960's, there are few analytical solutions available. By solving a non-homogeneous, modified Helmholtz equation in an infinite wedge, we find analytical solutions for the Laplace transforms of FPTs. We show that these Laplace transforms can be numerically inverted. The FPT problems lead to a class of bivariate exponential distributions which are absolute continuous but do not have memoryless property. We also prove that the density of the absolute difference of FPTs tends to infinity if and only if the correlation between the two Brownian motions is positive. This is a joint work with Haowen Zhong.

 

 

Bio:

Steven Kou is a Provost’s Chair Professor of Mathematics and the Director of the Risk Management Institute at the National University of Singapore. Previously, he taught at Columbia University, University of Michigan, and Rutgers University. He teaches courses in quantitative finance, stochastic models, and statistics. Currently he is a co-area-editor for Operations Research, and has served on editorial boards of Management Science, Mathematical Finance, Advances in Applied Probability, Mathematics of Operations Research, Operations Research Letters, Probability in Engineering and Information Science, Journal of Business and Economics Statistics, and Statistica Sinica. He is also the Vice President-Applied Probability for the Financial Service Section of INFORMS. He won the Erlang Prize from INFORMS.

 

 

This seminar is hosted by Prof. Nan Chen.

 

 

Venue: Room 513,

      William M.W. Mong Engineering Building (ERB),

      (Engineering Building Complex Phase 2)

      The Chinese University of Hong Kong.