The near-optimal maximum principle of impulse control for stochastic recursive system

Abstract

Here, we discuss the near-optimality for a class of stochastic impulse control problems. The state process in our problem is given by forward-backward stochastic differential equations (FBSDEs) with two control components involved: the regular and impulse control. More specially, the impulse control is defined on a sequence of prescribed stopping times. A recursive cost functional is introduced and the maximum principle for its near-optimality (both necessary and sufficient conditions) is derived with the help of Ekeland’s principle and variational analysis. For illustration, one concrete example is studied with our maximum principle and the corresponding near-optimal control is characterized.

概要

创新点

本文第一次较为系统的研究了关于随机递归系统的脉冲控制下的近似最大值原理, 获得了关于近似控制的几个可行的状态和输入的数学估计, 同时基于脉冲控制的特点, 讨论了精确最优控制和近似最优控制之间的差距的数学描述. 我们的状态可以用一个比较广泛的正倒向系统描述, 因此状态可以描述经济金融中广泛应用的随机递归效用. 由于需要处理倒向部分的状态变量, 所以我们的估计和分析同处理纯正向状态的讨论也有不同. 同时, 我们的工作也提供了一个基本视角可以用来讨论更为实际, 同时也更为困难的随机停止时间作为控制一部分输入的情况.