A Regression-Based Numerical Method for Forward-Backward Stochastic Differential Equations

We introduce a new class of basic functions based on characteristic functions to approximate two kinds of conditional expectations. we give the proofs and the error analysis of the approximations. In terms of such approximations, we employ a theta-discretization of time integrands for numerical solutions of forward-backward stochastic differential equations, and use Least-squares Monte Carlo simulations based on the basic functions. Numerical experiments are employed to show the algorithm available, and an empirical formula is pointed out for more general application