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A Regression Method Based on Characteristic Functions for Numerical Solutions of Forward-Backward Stochastic Differential Equations

In this paper, we develop a theta-discretization of time integrands for numerical solutions of forward-backward stochastic differential equations, and suggest a new set of basic functions to the Least -squares Monte Carlo simulations. This set of basic functions bases on characteristic functions of transitional densities. Numerical experiments are employed by showing the algorithm available, and a empirical formula is pointed out for more general application.