英文标题：
《Optimal Stopping under Model Ambiguity: a Time-Consistent Equilibrium
  Approach》
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作者：
Yu-Jui Huang, Xiang Yu
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最新提交年份：
2021
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英文摘要：
  An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\\alpha$-maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect equilibrium stopping policies, formulated as fixed points of an operator. For a one-dimensional diffusion with drift and volatility uncertainty, we show that every equilibrium can be obtained through a fixed-point iteration. This allows us to capture much more diverse behavior, depending on an agent\'s ambiguity attitude, beyond the standard worst-case (or best-case) analysis. In a concrete example of real options valuation under volatility uncertainty, all equilibrium stopping policies, as well as the best one among them, are fully characterized. It demonstrates explicitly the effect of ambiguity attitude on decision making: the more ambiguity-averse, the more eager to stop -- so as to withdraw from the uncertain environment. The main result hinges on a delicate analysis of continuous sample paths in the canonical space and the capacity theory. To resolve measurability issues, a generalized measurable projection theorem, new to the literature, is also established.
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中文摘要：
介绍了一种非常规的模型模糊下的最优停止方法。除了模糊性本身之外，我们还考虑了代理人对模糊性的厌恶程度。通过$\\ alpha$-maxmin非线性期望包含模糊态度，使得停止问题时间不一致。我们寻找子博弈完美均衡停止策略，将其表述为算子的不动点。对于具有漂移和波动不确定性的一维扩散问题，我们证明了每个平衡点都可以通过不动点迭代得到。这使我们能够捕捉到更多不同的行为，这取决于代理的模糊态度，超出了标准的最坏情况（或最佳情况）分析。在波动率不确定性下实物期权估值的一个具体例子中，充分描述了所有均衡停止策略，以及其中的最佳策略。它明确表明了模糊态度对决策的影响：越是厌恶模糊，就越渴望停止——从而从不确定的环境中退出。主要结果取决于正则空间中连续样本路径的精细分析和容量理论。为了解决可测性问题，还建立了一个新的广义可测投影定理。
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分类信息：

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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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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