To a forward-backward stochastic differential equation is naturally associated a quasilinear partial differential equation. In the spirit of the work of Gaeta, we develop a theory of symmetries for FBSDE's. These symmetries turn out to be related to the symmetries (in Olver's sense) of the corresponding quasilinear PDE. An analogous theory is developed for BSDE's.

This is joint work with Dr. Anas Ouknine (Rouen).