Shige Peng

BSDE and Reflected BSDE driven by G-Brownian Motion

Reflected Backward Stochastic Differential Equations (BSDE) is a sharp and powerful tool in various situations to analyze and calculate optimal stopping problems of a nonlinear high-dimensional system. Often the environments is so complex such that the model uncertainty cannot be negligible. In this situation one need to introduce a G-Brownian motion to robustly model the dynamic model uncertainty of the system.

In this talk we present our recent research results of reflected BSDE driven by G-Brownian motion with which we can treat the optimal stopping problem. We have found a very interesting formulation to describe such new type of reflected BSDE. Some fundamental results such as existence, uniqueness and comparison theorems, as well as a new type of probabilistic interpretation of the free-boundary problem for fully nonlinear parabolic PDE have been obtained under this framework.

It is also worth to mention that, since Fatou’s lemma is not available in this framework of G-expectation, we need to find a new approach to obtain the convergence in the construction of the solution. The construction can be used to get a numerical algorithm for high dimensional situations.

(This is a join work with Li Hanwu.)

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