The Basic Theory And Some Applications Of Backward Stochastic Differential Equatios

Shige Peng and Pardoux made pioneering contributions to the theories and applications of backward stochastic differential equations.Duffie and Epstein are famous economists and they introduced backward stochastic differential equations in economic terms in 1992,which made research on backward stochastic differential equations have economic background and received mathematicians' and economists'extensive attention and research.With the in-depth study,backward stochastic differential equations have very important applications in many subjects.In the respect of the partial differential equation,the solution of backward stochastic differential equations describes the partial differential equation.In the respect of the stochastic control,we can calculate current state according to risk status of future.In terms of filtering,we prove that the conditional expectation of the solutions of stochastic differential equations can be expressed through the solution of backward stochastic differential equations.Therefore.there is important value and significance of research on backward stochastic differential equations.Now we give the basic framework of this paper.The paper consists of five chapters.The first chapter is the introduction,which summarizes some important development and effects of backward stochastic differential equations.The second chapter mainly elaborates the connection between partial differential equations and backward stochastic differential equations and we can use the solution of backward stochastic differential equations to describe the partial differential equation.The third chapter proves the basic property of the solution of backward stochastic differential equation and describes its some applications.The fourth chapter introduces the basic theory and the application of backward stochastic differential equations.The fifth chapter introduces the basic theory of stationary backward stochastic differential equations.