Before revision:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator  , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
After revision:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator , 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 .