Dr. Nizar Touzi (Ecole Polytechnique, France)

Title: Wellposedness of Second Order Backward SDEs

Abstract: We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs. In particular, we provide a fully nonlinear extension of the Feynman-Kac formula. We discuss various applications to probabilistic numerical methods, and hedging under market illiquidity.