Talk by Jin Ma (USC)

Title: Recent Developments on Forward-backward Stochastic Differential Equations

Abstract: The theory of Backward Stochastic Differential Equations (BSDEs) and its more general form, Forward-backward Stochastic Differential Equations (FBSDEs), has been extensively studied for the past two decades, and its applications have been found in many branches of applied mathematics, in particular stochastic control theory and mathematical finance. However, it has been observed that in many applications the solvability of the FBSDEs involved is often beyond the scope of any currently existing frameworks, especially in the non-Markovian cases.

In this talk I will give a brief overview of the existing literature of FBSDEs, as well as some recent developments regarding the solvability of FBSDEs, especially in the non-Markovian cases with possible degenerate forward diffusions, which has been considered as longstanding problems in the literature. Some related topics in stochastic PDEs, in the spirit of the nonlinear Feynman-Kac formula, will also be discussed.