英文标题：
《Explicit Solution for Constrained Stochastic Linear-Quadratic Control
with Multiplicative Noise》
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作者：
Weipin Wu and Jianjun Gao and Duan Li and Yun Shi
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最新提交年份：
2017
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英文摘要：
We study in this paper a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piece-wise affine function of the state and can be computed off-line efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems.
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中文摘要：
本文研究了一类带乘性噪声的标量状态随机系统的约束线性二次型（LQ）最优控制问题，该问题在金融风险管理中有着广泛的应用。模型中考虑的控制变量和状态变量的线性约束破坏了传统LQ公式的优雅结构，并阻碍了文献中明确控制策略的推导。本文利用这类问题结构的状态分离性质，成功地导出了这类问题的解析控制策略。我们发现，最优控制策略是状态的分段仿射函数，可以通过求解两个耦合的Riccati方程离线有效地计算出来。在一些温和的条件下，我们还得到了无限时间范围内的平稳控制策略。我们通过一些示例演示了我们的方法的实现，并展示了如何校准我们的模型以解决动态约束投资组合优化问题。
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分类信息：

一级分类：Computer Science 计算机科学
二级分类：Systems and Control 系统与控制
分类描述：cs.SY is an alias for eess.SY. This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
cs.sy是eess.sy的别名。本部分包括理论和实验研究，涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制，以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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