论文标题
向后的二次控制，对向后随机微分方程，并具有部分信息
Linear Quadratic Control of Backward Stochastic Differential Equation with Partial Information
论文作者
论文摘要
在本文中，我们研究了在部分信息下具有二次成本功能的线性向后随机微分方程（BSDE）的最佳控制问题。通过使用随机最大原理和脱钩技术，可以完全明确地解决此问题。通过使用最大原理，可以获得带有滤波的前回前随机微分方程（FBSDE）的随机哈密顿系统。通过解开随机的哈密顿系统，三个Riccati方程，带过滤的BSDE和带有过滤的随机微分方程（SDE）。然后，我们获得具有反馈表示的最佳控制。还建立了相应最佳成本的明确公式。作为说明性示例，我们考虑了两个特殊的标量值控制问题，并给出一些数值模拟。
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic maximum principle and a decoupling technique. By using the maximum principle, a stochastic Hamiltonian system, which is a forward-backward stochastic differential equation (FBSDE) with filtering, is obtained. By decoupling the stochastic Hamiltonian system, three Riccati equations, a BSDE with filtering, and a stochastic differential equation (SDE) with filtering are derived. We then get an optimal control with a feedback representation. An explicit formula for the corresponding optimal cost is also established. As illustrative examples, we consider two special scalar-valued control problems and give some numerical simulations.
