Student Math Finance Seminar

I present a paper by Come Hure, Huyen Pham, and Xavier Warin, which introduces new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, the algorithms simultaneously estimate the solution and its gradient by deep neural networks. These approximations are performed at each time step by the minimization of loss functions defined recursively by backward induction. The methodology is then extended to variational inequalities arising in optimal stopping problems and applied to pricing American options. Finally, potential extensions to switching problems are discussed. Paper: https://arxiv.org/abs/1902.01599 Speaker(s): April Nellis (University of Michigan)