Forward-backward stochastic differential equations with nonsmooth coefficients

Solvability of forward-backward stochastic differential equations with nons mooth coefficients is considered using the Four-Step Scheme and some approx imation arguments. For the one-dimensional case, the existence of an adapte d solution is established for the equation which allows the diffusion in th e forward equation to be degenerate. As a byproduct, we obtain the existenc e of a viscosity solution to a one-dimensional nonsmooth degenerate quasili near parabolic partial differential equation. (C) 2000 Elsevier Science B.V . All rights reserved.