英文标题：
《Optimal Control of Conditional Value-at-Risk in Continuous Time》
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作者：
Christopher W. Miller, Insoon Yang
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最新提交年份：
2017
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英文摘要：
  We consider continuous-time stochastic optimal control problems featuring Conditional Value-at-Risk (CVaR) in the objective. The major difficulty in these problems arises from time-inconsistency, which prevents us from directly using dynamic programming. To resolve this challenge, we convert to an equivalent bilevel optimization problem in which the inner optimization problem is standard stochastic control. Furthermore, we provide conditions under which the outer objective function is convex and differentiable. We compute the outer objective\'s value via a Hamilton-Jacobi-Bellman equation and its gradient via the viscosity solution of a linear parabolic equation, which allows us to perform gradient descent. The significance of this result is that we provide an efficient dynamic programming-based algorithm for optimal control of CVaR without lifting the state-space. To broaden the applicability of the proposed algorithm, we propose convergent approximation schemes in cases where our key assumptions do not hold and characterize relevant suboptimality bounds. In addition, we extend our method to a more general class of risk metrics, which includes mean-variance and median-deviation. We also demonstrate a concrete application to portfolio optimization under CVaR constraints. Our results contribute an efficient framework for solving time-inconsistent CVaR-based sequential optimization.
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中文摘要：
我们考虑了目标函数中具有条件风险值（CVaR）的连续时间随机最优控制问题。这些问题的主要困难在于时间不一致性，这使我们无法直接使用动态规划。为了解决这个问题，我们将其转化为一个等价的双层优化问题，其中内部优化问题是标准随机控制。此外，我们还提供了外部目标函数凸可微的条件。我们通过Hamilton-Jacobi-Bellman方程计算外目标的值，并通过线性抛物方程的粘性解计算其梯度，这允许我们执行梯度下降。这个结果的意义在于，我们在不提升状态空间的情况下，为CVaR的最优控制提供了一种有效的基于动态规划的算法。为了扩大该算法的适用性，我们提出了在关键假设不满足相关次优界的情况下的收敛近似方案。此外，我们将我们的方法扩展到一类更一般的风险度量，包括均值-方差和中值-偏差。我们还展示了CVaR约束下投资组合优化的具体应用。我们的结果为解决基于时间不一致CVaR的序列优化问题提供了一个有效的框架。
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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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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