Numerical Method Of Reflected Backward Stochastic Differential Equations

Due to the structure of reflected backward stochastic differential equations(RBSDEs),it is widely used in the fields of stochastic control,mathematical finance and stochastic game.However,it is very difficult to give the exact solution of the equation.Therefore,it is of great application value to find a suitable approach system and give the numerical solution of the equation.In this thesis,we mainly study the Euler-Penalization system of RBSDE under Lipschitz.Firstly,the discrete approximation system is constructed by combining Euler method and penalty method,and the continuous form of the approximation system is given by using martingale representation theorem.The numerical solution of RBSDE using penalty method was first proposed by Pardoux and Karoui.They used BSDE without reflection term to approximate RBSDE,and analyzed the convergence of penalty approximation system.Zhang applied the Euler method to the study of the numerical solution of the BSDE,and obtained the error of the Euler method to construct the numerical approximation system of the BSDE.Secondly,we estimate the solution of Euler-Penalization scheme,and the convergence of Euler-Penalization scheme is analyzed.In this thesis,we conclude that the constructed Euler-Penalization system has mean square convergence when the Euler partition number n and the penalty coefficient m satisfy certain conditions.In conclusion,the combination of penalty method and Euler method to study the numerical approximation system of RBSDE widens the research scope of its numerical solution,and has important research significance for the practical application of RBSDE.