英文标题：
《On Positive Solutions of a Delay Equation Arising When Trading in
  Financial Markets》
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作者：
Chung-Han Hsieh, B. Ross Barmish, and John A. Gubner
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最新提交年份：
2019
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英文摘要：
  We consider a discrete-time, linear state equation with delay which arises as a model for a trader\'s account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain $\\alpha$ and a sequence $v(k)$ which models asset returns which are within known bounds but otherwise arbitrary. We introduce two thresholds, $\\alpha_-$ and $\\alpha_+$, depending on these bounds, and prove that for $\\alpha < \\alpha_-$, state positivity is guaranteed for all time and all asset-return sequences; i.e., bankruptcy is ruled out and positive solutions of the state equation are continuable indefinitely. On the other hand, for $\\alpha > \\alpha_+$, we show that there is always a sequence of asset returns for which the state fails to be positive for all time; i.e., along this sequence, bankruptcy is certain and the solution of the state equation ceases to be meaningful after some finite time. Finally, this paper also includes a conjecture which says that for the \"gap\" interval $\\alpha_- \\leq \\alpha \\leq \\alpha_+,$ state positivity is also guaranteed for all time. Support for the conjecture, both theoretical and computational, is provided.
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中文摘要：
我们考虑一个离散时间的线性时滞状态方程，该方程作为交易员在金融市场买卖风险资产时的账户价值模型。状态方程包括一个非负反馈增益$\\α$和一个序列$v（k）$，该序列对资产回报进行建模，这些资产回报在已知范围内，但在其他方面是任意的。根据这些界限，我们引入了两个阈值$\\ alpha\\u-$和$\\ alpha\\u+$，并证明了对于$\\ alpha<\\ alpha\\u-$，状态正性在所有时间和所有资产返回序列中都得到保证；i、 例如，破产被排除，状态方程的正解可以无限期地继续下去。另一方面，对于$\\ alpha>\\ alpha\\+$，我们证明了始终存在一系列资产回报，对于这些资产回报，状态并非始终为正；i、 沿着这个序列，破产是必然的，状态方程的解在一段有限的时间后就不再有意义了。最后，本文还包括一个猜想，即对于“gap”区间$\\ alpha\\u-\\ leq\\alpha\\leq\\alpha\\u+，$状态也始终是正的。本文从理论和计算两方面对这一猜想提供了支持。
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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：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Systems and Control        系统与控制
分类描述：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.
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：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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