The Discrete Backward Stochastic Differential Equations With Improved Euler Method

The study on discretization and convergence of BSDE rapidly developed in recent years. The numerical solution of BSDE is essentially different from the classical forward SDE. Some linear BSDE can be solved by using Monte-Carlo method. From nonlinear cases, by nonlinear Feymann-Kac formula,the numerical methods for PDE can be applied to solve certain BSDEs.This master's thesis use the scaled random walk to approximate the corresponding Brownian Motion by using of the weak convergence of filtrations from the left_node stochastic method, we proposed right_node and trapezoid stochastic method, proved the exist and unique of the solution of the corresponding discrete BSDE and its convergence and stability by using of the two method. Moreover we given the scheme of the solution and simulation results. Furthermore, the proposed numerical methods are applied to discuss financial models. We used the improved Euler methods to pricing of the contingent claims in complete market. Finally, we discussed the exist and unique and convergence of the discretesolution of the BSDE under local Lipschitz condition.