Using 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 and backward iterations of the superquadratic BSDE. The superquadratic BSDE in this article includes quadratic BSDEs appear in stochastic differential game and price impact model. Our result also provides the well-posedness of a system of path-dependent quasilinear PDE that generalizes Ladyzhenskaia and Uraltseva (1968).
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