Before revision:  By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out  recursive approximation to an arbitrarily higher order, where the required calculations in each order are equivalent to those for the standard European contingent claims.
After revision:  By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily higher order, where the required calculations in each order are equivalent to those for the standard European contingent claims.