发表机构
Kyoto University（京都大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种对偶方法刻画强Feller过程的最优停时问题，适用于一维及多维马尔可夫过程，并解决了停时区域为两个不相交连通分量的难题。
AI 中文摘要
我们提出了一种新颖的对偶方法，用于刻画局部紧可分度量空间上强Feller过程的最优停时问题的解。我们的刻画基于将最优停时理论中的一个标准结果重新解释为对偶形式，从而产生计算上可处理的算法。我们的框架适用于一大类马尔可夫过程。首先，在一维情形下，以往研究仅能在无限时间区间上全面解决扩散过程和单边跳跃Lévy过程，而我们的方法成功地将这些过程扩展到无限和有限时间区间，包括双边跳跃Lévy过程。此外，对于多维情形，我们的框架适用于具有某些结构特征（如凸停时区域）的无限时间区间上的扩散过程。为了说明这种通用性，我们明确解决了几个具有挑战性的问题，包括一个最优停时区域由两个不相交连通分量组成的情形——这一结构特征在文献中尚未被解决。
英文摘要
We present a novel dual approach to characterizing the solution to optimal stopping problems for strong Feller processes on locally compact, separable metric spaces. Our characterization builds upon reinterpreting a standard result in optimal stopping theory as a dual formulation, which yields computationally tractable algorithms. Our framework is applicable to a broad class of Markov processes. First, in the one-dimensional case, while previous studies have managed to comprehensively solve only diffusion and one-sided jump Lévy processes over an infinite time horizon, our proposed method successfully extends to both infinite- and finite-horizon scenarios across all these processes, including two-sided jump Lévy processes. In addition, for multi-dimensional cases, our framework is applicable to diffusions over an infinite horizon with certain structural features such as convex stopping regions. To illustrate this versatility, we explicitly solve several challenging problems including a case where the optimal stopping region consists of two disjoint connected components -- a structural feature that remains unaddressed in the literature.
