  In this paper, we propose an efficient Monte Carlo implementation of
non-linear FBSDEs as a system of interacting particles inspired by the ideas of
branching diffusion method. It will be particularly useful to investigate large
and complex systems, and hence it is a good complement of our previous work
presenting an analytical perturbation procedure for generic non-linear FBSDEs.
There appear multiple species of particles, where the first one follows the
diffusion of the original underlying state, and the others the Malliavin
derivatives with a grading structure. The number of branching points are capped
by the order of perturbation, which is expected to make the scheme less
numerically intensive. The proposed method can be applied to semi-linear
problems, such as American and Bermudan options, Credit Value Adjustment (CVA),
and even fully non-linear issues, such as the optimal portfolio problems in
incomplete and/or constrained markets, feedbacks from large investors, and also
the analysis of various risk measures.
