Backward Stochastic Differential Equations And Its Applications

In 1973,the linear backward stochastic differential equation was first proposed by J.M.Bismut.Subsequently,Pardoux and Peng have extended it to its nonlinear case,have presented and proved the existence and uniqueness of solutions for backward s-tochastic differential equations.In this paper,we present the general conclusions of the backward stochastic differential equation,such as the existence and uniqueness theorem of the solution and the comparison theorem,and the existence condition of the weaken-ing solution,and present applications of backward stochastic differential equations in financial mathematics,optimal control.This paper is mainly composed of the following parts:The chapter 1 introduces the development of the backward stochastic differential equation and its related scholarly papers,and made a brief introduction of this paper and its economic applicationThe chapter 2 presents some general conclusions of the backward stochastic d-ifferential equation,such as the existence and uniqueness theorem of solutions under Lipschitz coefficients,the representation theorem and the comparison theorem of solu-tions in linear case.The chapter 3 gives the application of backward stochastic differential equation in finance and optimal control.In chapter 4,we introduce the Markov condition,the backward stochastic differential equation under the condition of second order growth,and have weaken the existence of the solution condition.Finally,in Chapter 5,we introduce the application of reflection backward stochastic differential equation and American option pricing problem.