This research project concerns development of new numerical methods for stochastic partial differential equations and their application to mathematical finance. These applications include option hedging and pricing, stochastic volatility models, computation of value-at-risk, asset management, and interest rate term structure modeling.
On one hand, this research will combine techniques including control theory, high-performance computing, Ito analysis, and Malliavin calculus to numerically solve sophisticated random systems. On the other hand, it will provide better understanding of a central problem in finance, namely, crossing the bridge from discrete time models to continuous time ones. This work has potential to improve the practical implementation of mathematical models in the finance industry, with resultant increase in efficiency and decrease in the probability of financial crisis.
