倒向随机微分方程的研究与应用

Research and Application of Backward Stochastic Differential Equations

倒向随机微分方程在随机微分对策、随机最优控制、偏微分方程以及金融数学等方面的应用中起到了重要的作用。本文阐述了倒向随机微分方程的基本原理,对它的一般性结论进行说明。提出倒向随机微分方程在最优控制中的应用,给出倒向随机微分方程最优控制的数学模型,并给出在最优控制问题中的条件假设以及状态方程,并对其最优性进行了相关的证明。

Backward stochastic differential equations plays an important role in the applications of game,stochastic optimal control,partial differential equations and financial mathematics.In this paper,the basic principle of backward stochastic diferential equation is descrilDed,and its general conclusion is explained.The application of backward stochastic diferential equations in optimal control is presented.A mathiematical model for optimal control of backward stochastic diferential equations is given.The conditional assumptions and state equations in optimal given,and their optimality is proved.