Global Well-posedness of Non-Markovian Multidimensional Superquadratic BSDE

Abstract: (Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backward stochastic differential equations (FBSDEs) and backward iterations of the superquadratic BSDE. The superquadratic BSDE studied in this article includes quadratic BSDEs appear in stochastic differential game and price impact model. We also study the well-posedness of superquadratic FBSDEs and FBSDEs with measurable coefficients using the corresponding BSDE results. Our result also provides the well-posedness of a system of path-dependent quasilinear partial differential equations where the nonlinearity has superquadratic growth in the gradient of the solution.