On the numerical solution of Backward Stochastic Differential Equations

We study the problem of the numerical solution to BSDEs from a weak approximation viewpoint. The first step is to build the framework that represents the approximating step processes (Yp, Zp) as iterations of a certain family of operators. We then state an assumption that catches the error induced on the algorithm by the method one uses to compute the involved conditional expectations. This provides us with a global rate of convergence. As a first example we present the Malliavin calculus method. For this one we also suggest ways to simplify the complexity of the weights used in the Monte Carlo simulations. Next we apply the cubature method to compute the conditional expectations. The latter is more illustrating as how one may depart from the standard practice of using an Euler scheme for the underlying process and Monte Carlo methods in the simulation of the random variables.