摘要翻译：
我们研究了一个关于相互奇异概率集$\cp$的鲁棒最优停止问题。这可以被解释为一个零和控制器-塞子博弈，塞子试图最大化其收益，而对手希望通过从$\CP$中选择一个评价标准来最小化该收益。我们证明了奖励过程$Y$的\emph{upper Snell信封$\ol{Z}$}是一个关于适当定义的非线性期望$\ul{\se}$的上鞅，并且$\ol{Z}$是一个直到$\t^*$第一次$\ol{\se}$满足$Y$时的$\ul{\se}-$鞅。因此，$\t^*$是鲁棒最优停止问题的最优停止时间，相应的零和对策有一个值。虽然与经典最优停止理论的结果相似，但概率的相互奇异性和问题的博弈方面引起了主要的技术障碍，我们使用一些新的方法来规避这些障碍。
---
英文标题：
《On the Robust Optimal Stopping Problem》
---
作者：
Erhan Bayraktar and Song Yao
---
最新提交年份：
2014
---
分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
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。
--
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
--
一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
--

---
英文摘要：
  We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from $\cP$. We show that the \emph{upper Snell envelope $\ol{Z}$} of the reward process $Y$ is a supermartingale with respect to an appropriately defined nonlinear expectation $\ul{\sE}$, and $\ol{Z}$ is further an $\ul{\sE}-$martingale up to the first time $\t^*$ when $\ol{Z}$ meets $Y$. Consequently, $\t^*$ is the optimal stopping time for the robust optimal stopping problem and the corresponding zero-sum game has a value. Although the result seems similar to the one obtained in the classical optimal stopping theory, the mutual singularity of probabilities and the game aspect of the problem give rise to major technical hurdles, which we circumvent using some new methods.
---
PDF链接：
https://arxiv.org/pdf/1301.0091