Equilibrium for Time-Inconsistent Stochastic Linear–Quadratic Control under Constraint
Equilibrium for Time-Inconsistent Stochastic Linear–Quadratic Control under Constraint
复制标题
约束下时间不一致随机线性二次控制的平衡
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Xunjing Li
中科院分区：
文献类型：
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作者：
Ying Hu;Jianhui Huang;Xunjing Li
本文研究了一类具有控制输入约束的随机时不一致线性二次控制问题。这些问题是在与随机系数相关的更一般的框架内研究的。本文旨在进一步发展一种与文献中标准控制（无约束）理论根本不同的新方法，以应对由于输入约束的存在而产生的数学困难。首先证明了一类带约束的正反向随机微分方程的平衡解的存在性等价于其解的存在性。在凸锥约束下，得到了均值-方差投资组合均衡的显式解，并证明了其唯一性。最后，讨论了一些例子，以说明我们所建立的结果与标准控制理论的比较。
In this paper, we study a class of stochastic time-inconsistent linear-quadratic (LQ) control problems with control input constraints. These problems are investigated within the more general framework associated with random coefficients. This paper aims to further develop a new methodology, which fundamentally differs from those in the standard control (without constraints) theory in the literature, to cope with the mathematical difficulties raised due to the presence of input constraints. We first prove that the existence of an equilibrium solution is equivalent to the existence of a solution to some forward-backward stochastic differential equations with constraints. Under convex cone constraint, an explicit solution to equilibrium for mean-variance portfolio selection can be obtained and proved to be unique. Finally, some examples are discussed to shed light on the comparison between our established results and standard control theory.