| Forward backward stochastic differential equations(FBSDEs)composed of forward stochastic differential equation given initial conditions in probability space and backward stochastic differential equation given final conditions.This type of equations aimed at reaching final conditions from the initial conditions with random noisy in the environment.Natural phenomenon can be described more reasonable and approximated with better precision using forward backward stochastic differential equations.It has been applied to multiple fields,including financial mathematics,game theory and stochastic control,etc.However,an analytical solution is hard to obtained for most of the problems we're interested.The importance of analysis and construction of numerical methods revealed itself under such circumstances.In this thesis,we present two iterative methods based on one step multiderivative method and compounded ?-method.There are five sections in total.In the first chapter,we give a brief introduction to the background of theoretical analysis of FBSDEs,numerous applications of FBSDEs,and a survey of current research progress on FBSDEs from domestic to overseas.In the meantime,contribution of this thesis will also be presented.The fundamental results regarding stochastic differential equations and backward differential equations,and integral formula of Gauss-Hermite are included in the second chapter.In the third chapter,novel iterative method based on one step multi-derivative method will be analyzed.Through the comparison between numerical results from linear ?-method and this method,the superiority of this method in precision and effectiveness can be proofed.Another method based on compounded ?-method is also analyzed in the forth chapter.Numerical results along with theoretical analysis are listed in this chapter.In the last chapter,summarization of this thesis and future work for FBSDEs.Possible directions for further study are also discussed. |
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