论文标题
扩展动态编程原则和对时间不一致的控制的应用
Extended Dynamic Programming Principle and Applications to Time-Inconsistent Control
论文作者
论文摘要
由于Peng（1993）建立了由前向后的随机微分方程（FBSDES）控制的一般随机控制问题的局部最大原理，因此尚未开发相应的偏微分方程（PDE）表征。主要困难源于此类控制问题固有的潜在时间不一致。在尺寸增强的空间中，我们首先建立了扩展的动态编程原理（DPP）。因此，得出了扩展的汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程。还研究了该扩展的HJB方程的新型粘度解决方案的存在和独特性。与关于随机最大原理的现有研究相比，本文是对控制系统的PDE方法上的第一项正常工作，该系统的前进和后向方式都在状态发展。有趣的是，我们的扩展DPP为与传统的均值差异模型，风险敏感控制和效用优化相关的一般时间不一致的控制问题提供了平衡解决方案。
Since Peng (1993) established a local maximum principle for a general stochastic control problem governed by forward-backward stochastic differential equations (FBSDEs), the corresponding partial differential equation (PDE) characterization has not been developed yet. The main difficulty stems from the potential time inconsistency inherent in this class of control problems. In a dimension-augmented space, we first establish an extended dynamic programming principle (DPP). Consequently, an extended Hamilton-Jacobi-Bellman (HJB) equation is derived. The existence and uniqueness of a new type of viscosity solution is also investigated for this extended HJB equation. Compared to extant research on the stochastic maximum principle, the present paper is the first normal work on the PDE method for a control system with states evolving in both forward and backward manners. Interestingly, our extended DPP provides an equilibrium solution for general time-inconsistent control problems associated with the traditional mean-variance model, risk-sensitive control and utility optimization for narrow framing investors, among others.
