Maximum Principle for Forward-Backward Control System Driven by Ito-Levy Processes under Initial-Terminal Constraints

Liu Meijuan; Wang Xiangrong; Huang Hong

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Maximum Principle for Forward-Backward Control System Driven by Ito-Levy Processes under Initial-Terminal Constraints

机译：初始终端约束下由Ito-Levy过程驱动的向前-向后控制系统的最大原理

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This paper investigates a stochastic optimal control problem where the control system is driven by Ito-Levy process. We prove the necessary condition about existence of optimal control for stochastic system by using traditional variational technique under the assumption that control domain is convex. We require that forward-backward stochastic differential equations (FBSDE) be fully coupled, and the control variable is allowed to enter both diffusion and jump coefficient. Moreover, we also require that the initial-terminal state be constrained. Finally, as an application to finance, we show an example of recursive consumption utility optimization problem to illustrate the practicability of our result.

机译：本文研究了一个随机最优控制问题，其中控制系统由伊藤征税过程驱动。在控制域是凸的前提下，利用传统的变分技术，证明了存在随机系统最优控制的必要条件。我们要求前向-后向随机微分方程（FBSDE）完全耦合，并且允许控制变量输入扩散系数和跳跃系数。此外，我们还要求限制初始末端状态。最后，作为金融应用程序，我们展示了一个递归消费效用优化问题的例子，以说明我们的结果的实用性。

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来源
《Mathematical Problems in Engineering》 |2017年第6期|1868560.1-1868560.13|共13页
作者
Liu Meijuan; Wang Xiangrong; Huang Hong;
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Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

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1. A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints [J] . ShaolinJi, QingmengWei, XiuminZhang Abstract and applied analysis . 2012,第1期

机译：具有初始终端状态约束的时间对称的正反双随机微分方程的最大原理
2. A Maximum Principle for Fully Coupled Forward-Backward Stochastic Control System Driven by Lévy Process with Terminal State Constraints [J] . HUANG Hong, WANG Xiangrong, LIU Meijuan 系统科学与复杂性：英文版 . 2018,第004期

机译：具有最终状态约束的Lévy过程驱动的前向后向完全耦合随机控制系统的最大原理
3. A maximum principle for fully coupled forward-backward stochastic control systems with terminal state constraints [J] . Ji S., Wei Q. Journal of Mathematical Analysis and Applications . 2013,第2期

机译：具有终端状态约束的全耦合前向-后向随机控制系统的最大原理
4. Necessary conditions of forward-backward stochastic control system with initial-terminal constraints [C] . MeiJuan Liu, XiangRong Wang Chinese Control Conference . 2016

机译：具有初始终端约束的前向-后向随机控制系统的必要条件
5. Realizable constraint driven capacitor placement and control sequences for voltage spread reduction in distribution systems. [D] . Segal, Nicole Urim. 2015

机译：可实现的约束驱动电容器布局和控制序列，可降低配电系统中的电压分布。
6. Maximum principle for a stochastic delayed system involving terminal state constraints [O] . Jiaqiang Wen, Yufeng Shi -1

机译：具有终端状态约束的随机时滞系统的最大原理
7. A maximum principle for controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints [O] . Ji, Shaolin, Wei, Qingmeng, Zhang, Xiumin 2012

机译：受控时间对称前向后的最大原理具有初始终端状态的双随机微分方程限制

Maximum Principle for Forward-Backward Control System Driven by Ito-Levy Processes under Initial-Terminal Constraints

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