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Optimal stopping under model ambiguity: A time-consistent equilibrium approach
Mathematical Finance ( IF 1.6 ) Pub Date : 2021-04-19 , DOI: 10.1111/mafi.12312 Yu‐Jui Huang 1 , Xiang Yu 2
Mathematical Finance ( IF 1.6 ) Pub Date : 2021-04-19 , DOI: 10.1111/mafi.12312 Yu‐Jui Huang 1 , Xiang Yu 2
Affiliation
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 -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 any initial stopping policy will converge to an equilibrium 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 model ambiguity, all equilibrium stopping policies, as well as the best one among them, are fully characterized under appropriate conditions. 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.
中文翻译:
模型模糊下的最优停止:时间一致的均衡方法
介绍了一种在模型模糊下进行最优停止的非常规方法。除了歧义本身,我们还考虑了代理的歧义厌恶程度。这种包含歧义的态度,通过-maxmin 非线性期望,使停止问题时间不一致。我们寻找子博弈完美均衡停止策略,表述为算子的不动点。对于具有漂移和波动性不确定性的一维扩散,我们表明任何初始停止策略都将通过定点迭代收敛到均衡。这使我们能够根据代理的歧义态度捕获更多不同的行为,超出标准的最坏情况(或最佳情况)分析。在模型模糊下实物期权估值的一个具体例子中,所有均衡停止策略,以及最好的其中之一,在适当的条件下完全表征。它明确地展示了歧义态度对决策的影响:越厌恶歧义,就越渴望停下来——以便从不确定的环境中退出。主要结果取决于对规范空间中连续样本路径和容量理论的精细分析。为了解决可测量性问题,还建立了文献中新出现的广义可测量投影定理。
更新日期:2021-06-14
中文翻译:
模型模糊下的最优停止:时间一致的均衡方法
介绍了一种在模型模糊下进行最优停止的非常规方法。除了歧义本身,我们还考虑了代理的歧义厌恶程度。这种包含歧义的态度,通过-maxmin 非线性期望,使停止问题时间不一致。我们寻找子博弈完美均衡停止策略,表述为算子的不动点。对于具有漂移和波动性不确定性的一维扩散,我们表明任何初始停止策略都将通过定点迭代收敛到均衡。这使我们能够根据代理的歧义态度捕获更多不同的行为,超出标准的最坏情况(或最佳情况)分析。在模型模糊下实物期权估值的一个具体例子中,所有均衡停止策略,以及最好的其中之一,在适当的条件下完全表征。它明确地展示了歧义态度对决策的影响:越厌恶歧义,就越渴望停下来——以便从不确定的环境中退出。主要结果取决于对规范空间中连续样本路径和容量理论的精细分析。为了解决可测量性问题,还建立了文献中新出现的广义可测量投影定理。