发表机构
The Hong Kong Polytechnic University（香港理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对时间不一致停止问题提出惩罚方法，建立惩罚PDE解局部 $W^{2,1}_{p}$ 收敛性，并在凹性假设下证明控制问题收敛，数值示例验证理论。
AI 中文摘要
本文研究了一类一般的时间不一致停止问题的惩罚方法。受最优停止问题惩罚方法的一些现有结果的启发，我们为时间不一致停止问题引入了惩罚PDE问题和惩罚控制问题，揭示了由时间不一致性引起的一些有趣的差异。当惩罚趋于无穷大时，我们发展了一些新颖的论证，严格建立了惩罚PDE问题的解局部 $W^{2,1}_{p}$ 收敛到与时间不一致停止问题相关的变分不等式的解。在额外的凹性假设下，我们进一步推导了惩罚时间不一致控制问题收敛到时间不一致停止问题。我们重新审视了两个时间不一致停止的例子，以数值方式说明收敛理论。
英文摘要
This paper studies the penalization method for a general class of time-inconsistent stopping problems. Inspired by some existing results on penalization for optimal stopping problems, we introduce the penalized PDE problem and the penalized control problem for time-inconsistent stopping problems, uncovering some interesting discrepancy stemming from the time-inconsistency. As the penalization tends to infinity, we develop some novel arguments to rigorously establish the local $W^{2,1}_{p}$ convergence results for the solution of the penalized PDE problem to a solution of the variational inequality associated to the time-inconsistent stopping problem. Under an additional concavity assumption, we further derive the convergence of the penalized time-inconsistent control problem to the time-inconsistent stopping problem. We revisit two examples of time-inconsistent stopping to numerically illustrate the convergence theory.
