University of Pittsburgh |
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My research interests are in Applied Mathematics, especially in the application of methods of Functional Analysis, Asymptotic Analysis and Numerical Simulation to problems that are modeled by Partial Differential Equations. Most recently, I have been studying Free Boundary Value Problems that arise in a wide variety of applications (Solidification, Reservoir Dynamics, Waste Remediation and Finance). These interests have carried over to my teaching. I am actively involved in developing and teaching graduate courses in Mathematical Finance as well as the two mainstream courses in our new BS program in Actuarial Mathematics. |
Research supported by NSF award DMS-0707953.
Some of my recent preprints:
Written in collaboration with Xinfu Chen.
Written in collaboration with Xinfu Chen.
Written in collaboration with Xinfu Chen, Lishang Jiang, and Weian Zheng.
Written in collaboration with Lan Cheng, Xinfu Chen, and David Saunders.
Written in collaboration with Lan Cheng, Xinfu Chen, and David Saunders.
Written in collaboration with Changsheng Chen.
Written in collaboration with Dejun Xie and Xinfu Chen.
Written in collaboration with Junming Huang, Bo Shi, and Lung Kwan Tsui.
Analytical and Numerical Approximations for the Early Exercise
Boundary for American Put Options.
A Mathematical Analysis of the Optimal Exercise
Boundary for American Put Options.
SIAM J. Mathematical Analysis 38, 1613-1641, 2006.
Convexity of the Exercise Boundary of the
American Put Option on a Zero Dividend Asset.
Mathematical Finance 18, 185-197, 2008. Analysis of an Inverse First Passage Problem from Risk
Management.
SIAM J. Mathematical Analysis 38, 845-873, 2006.
Numerical Computation of a First Crossing Boundary Problem.
Bioremediation of Waste in a Porous Medium.
Appeared in 'Bifurcations and Pattern Formation,' vol. 49, Fields Institute Communications, Nagata and Namachchivaya, eds. (2006).
Optimal Prepayment of Mortgages
European Journal of Applied Mathematics 18, 363-388, 2007.
Comparison of Credit Default Models.
Integral Equation Methods for Free Boundary Problems.
To appear in Encyclopedia of Quantitative Finance.
Non-Convexity of the Optimal Exercise Boundary for an American Put Option on a Dividend-paying asset.
Submitted for publication.