Numerical Solutions for a Class of Backward Stochastic Differential Equations

We propose a method for numerical approximation of the solutions of backward stochastic differential equations in some non-lipschitz conditions for the coefficient functions and without the condition of the continuity for the final data. Given a simulation-based estimator of the conditional expectation operator, we then suggest a backward simulation scheme. Our explicitly method is simple to implement and it relies on approximation of Brownian motion by simple random walk.