摘要翻译：
研究了零和对策$\inf_{\tau}\sup_pe^p[x_{\tau}]$中最优行为的存在性。这包括一类次线性期望$\mathcal{E}(\cdot)$的最优停止问题$\inf_{\tau}\mathcal{E}(X_{\tau}）$。我们表明游戏有价值。利用次线性期望理论，我们定义了一个非线性Snell包络，并证明了首次命中时间$\inf{t:y_t=x_t\}$是一个最优停止时间。在紧性条件下证明了鞍点的存在性。最后，将所得结果应用于波动率不确定性下美式期权的次级套期保值。
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英文标题：
《Optimal stopping under adverse nonlinear expectation and related games》
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作者：
Marcel Nutz, Jianfeng Zhang
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最新提交年份：
2015
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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：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
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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
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英文摘要：
  We study the existence of optimal actions in a zero-sum game $\inf_{\tau}\sup_PE^P[X_{\tau}]$ between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem $\inf_{\tau}\mathcal{E}(X_{\tau})$ for a class of sublinear expectations $\mathcal{E}(\cdot)$ such as the $G$-expectation. We show that the game has a value. Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope $Y$ and prove that the first hitting time $\inf\{t:Y_t=X_t\}$ is an optimal stopping time. The existence of a saddle point is shown under a compactness condition. Finally, the results are applied to the subhedging of American options under volatility uncertainty.
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PDF链接：
https://arxiv.org/pdf/1212.2140