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Infinite Horizon Forward-Backward SDEs and Open-Loop Optimal Controls for Stochastic Linear-Quadratic Problems with Random Coefficients
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2021-07-13 , DOI: 10.1137/20m1360517 Qingmeng Wei , Zhiyong Yu
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2021-07-13 , DOI: 10.1137/20m1360517 Qingmeng Wei , Zhiyong Yu
SIAM Journal on Control and Optimization, Volume 59, Issue 4, Page 2594-2623, January 2021.
In this paper, we introduce a new infinite horizon domination-monotonicity framework. In this framework, by the method of continuation and some subtle techniques, we obtain an existence and uniqueness result and a pair of estimates for the solutions to a kind of infinite horizon coupled forward-backward stochastic differential equations (FBSDEs). Then, the theoretical result of FBSDEs is applied to solve a stochastic linear-quadratic (LQ) optimal control problem with random time-varying coefficients on infinite horizon. The unique open-loop optimal control is characterized by the solution of an infinite horizon FBSDE. Moreover, we find and illustrate a different phenomenon between the LQ problems on infinite horizon and finite horizon.
中文翻译：
具有随机系数的随机线性二次问题的无限视野前向-后向 SDE 和开环最优控制
SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2594-2623 页，2021 年 1 月。
在本文中，我们引入了一个新的无限视界支配-单调框架。在这个框架中，通过延拓法和一些微妙的技巧，我们获得了一种无限水平耦合前向后向随机微分方程（FBSDE）的解的存在唯一性结果和一对估计。然后，将 FBSDE 的理论结果应用于解决具有无限范围内随机时变系数的随机线性二次 (LQ) 最优控制问题。独特的开环最优控制的特点是无限水平 FBSDE 的解决方案。此外，我们发现并说明了无限视界和有限视界上的 LQ 问题之间的不同现象。
更新日期：2021-07-14
In this paper, we introduce a new infinite horizon domination-monotonicity framework. In this framework, by the method of continuation and some subtle techniques, we obtain an existence and uniqueness result and a pair of estimates for the solutions to a kind of infinite horizon coupled forward-backward stochastic differential equations (FBSDEs). Then, the theoretical result of FBSDEs is applied to solve a stochastic linear-quadratic (LQ) optimal control problem with random time-varying coefficients on infinite horizon. The unique open-loop optimal control is characterized by the solution of an infinite horizon FBSDE. Moreover, we find and illustrate a different phenomenon between the LQ problems on infinite horizon and finite horizon.
中文翻译：
具有随机系数的随机线性二次问题的无限视野前向-后向 SDE 和开环最优控制
SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2594-2623 页，2021 年 1 月。
在本文中，我们引入了一个新的无限视界支配-单调框架。在这个框架中，通过延拓法和一些微妙的技巧，我们获得了一种无限水平耦合前向后向随机微分方程（FBSDE）的解的存在唯一性结果和一对估计。然后，将 FBSDE 的理论结果应用于解决具有无限范围内随机时变系数的随机线性二次 (LQ) 最优控制问题。独特的开环最优控制的特点是无限水平 FBSDE 的解决方案。此外，我们发现并说明了无限视界和有限视界上的 LQ 问题之间的不同现象。
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