倒向随机微分方程及其应用

本文将介绍一类新的议程：倒向随机微分方程，为了便于理解，我们将首先通过与常微分方程和经典的随机微分方程的对比，并通过数理经济和数学金融学中的一个典型的例子来引入倒向随机微分方程。     

The existence problem of optimal control for nonlinear processes

The existence problem of optimal control systemsdescribed by z=f(t,x.u)is discussed in this paper,where f(f,x,u)is a more general function and theclass of admissible control functions are generalenough to contain those control functions which arefrequently used in engineering.The problem for anoptimal control approximated by a sequence of controlfunctions being part of certain function classes isconsidered here,an example in contradiction with theconclusion of ref.[1]about this problem is given,and a correct conclusion is presented.     

不确定情况下的一类递归效用优化问题(英文)

本文通过对倒向随机微分方程进行摄动的方法研究了金融市场中最优投资组合和消费选择问题．在没有凸性假设下,用Ｅｋｌａｎｄ 变分原理解决了这个带初始约束的优化问题     

A GLOBAL REPRESENTATION OF ALL SOLUTIONS TO A NONLINEAR EQUATION AND ITS APPLICATIONS

For a nonlinear equation, a global representation for all solutions is obtained. Via this represention, a nonlinear generalized inverse theorem is derived and an application to control systems with mixture constraints is given as well.     

关于非线性过程最优控制的存在性问题

本文讨论了形为x=f(t,x,u)的系统的最优控制的存在性问题,f(f,x,u)是比较一般的非线性函数,控制类普遍到足以包含一般工程上常见的控制函数.还讨论了由属于一定函数类的控制函数序列去逼近最优控制的问题,举出了与文[1]结论相矛盾的反例,并导出这问题的正确结论.