Backward Stochastic Differential Equations And Applications To Optimal Control

In real life,we often encounter such a problem:how to determine the current state and implementation strategy for a future expectation aim,and BSDE is a very important way to solve such problems.At the same time,BSDE is also an effective tool for studying PDE,stochastic control,computer science and other fields.BSDE has become one of the important branches of stochastic analysis.This paper is a summary report on the existence and uniqueness of solutions for a class of BSDE under local Lipschitz conditions,and the stochastic optimal control prob-lem associated with them-the maximum principle.The details are as follows:the first chapter mainly introduces the development history,the research status and theoretical significance of BSDE.The second chapter is about the preliminary knowledge involved in this paper.In the third chapter,we study the existence and uniqueness of global solu-tions for a class of BSDE under the local Lipschitz conditions.The existence of global solutions for a class of generalized Riccati equation with random coefficients is given in Chapter 4.The fifth chapter gives the stochastic maximum principle of the optimal control system of forward and backward state equations.The sixth chapter reviews the main conclusion.