Probabilistic Numerical Methods for Fully Nonlinear Parabolic PDEs

Start: 04/19/2012 - 4:15pm
End  : 04/19/2012 - 5:15pm

Statistics/OR/Math Finance Seminar

Jianfeng Zhang (USC)


Motivated by the remarkable work Fahim, Touzi, and Warin (2010), we introduce a probabilistic numerical method for fully nonlinear parabolic PDEs in this talk. By using certain trinomial tree instead of Brownian Motion, we remove a serious bound constraint imposed in Fahim, Touzi, and Warin (2010).  Our scheme works well for high dimensional PDEs with a diagonal dominant coefficient of the Hessian matrix, and it is fast and stable when the dimension is low (d<=3). As a special case, our scheme can be applied to solve high dimensional coupled FBSDEs, especially when the forward diffusion is diagonal.  We will show several numerical examples, with dimension up to 12. The talk is based on a joint work with Wenjie Guo and Jia Zhuo.



Davidson Lecture Hall, Claremont McKenna College