Dr. Shige Peng (Shandong University, Global Scholar of Princeton)

Title: BSDE, PDE, Nonlinear Expectation and Model Uncertainty

Abstract:Nonlinear Feynman-Kac formula tells us that, when the coefficients depend only on the state of the path of a Brownian, then a Backward Stochastic Differential Equation (BSDE) becomes a quasilinear PDE of parabolic type. This reveals that, in general, a BSDE is in fact a new type of PDE called path dependent PDE, in which the continuous path plays the role of state variable x. The nonlinear semigroup associated to this PDE is a nonlinear expectation.

We have also established the fully nonlinear parabolic PDE and corresponding paths of G-Brownian motion which is continuous paths under a fully nonlinear G-expectation, an important tool to measure risk for under probability and/or distribution uncertainties.