Some Numerical Methods Of Backward Doubly Stochastic Differential Equations

The theory of BSDE is rapidly developed in recent years and has been more and moreapplication to finance. In 1994 Pardoux and Peng brought forward a new kind of BSDE calledbackward doubly stochastic differential equation (BDSDE for short). They also proved theexistence and uniqueness of solution to BDSDE under the uniformly lipschitz conditions.Meanwhile, the study on discretization and convergence of BSDE is also developedrapidly. As the analytic solution of many BSDEs can not be obtained, the study ondiscretization of BSDE has important sense in theory and application. This master's thesis usethe random walk to approximate the corresponding Brownian Motion. We take the advantageof the different kinds of Euler methods to obtain several numerical methods of discreteBDSDE and prove the convergence and stability.The paper is consisted of four parts. The first chapter introduces the background and theresearch value of the project together with the structure and main results of the paper. In thesecond chapter, we prove the convergence of the solution of discrete BDSDE by using of thedifferent kinds of Euler methods. The third chapter presents the stability of discrete BDSDE.In chapter 4 we discuss the existence and uniqueness of the solution of BDSDE under localLipchitz conditions.