Theory of Probability &Its Applications, Volume 65, Issue 3, Page 341-358, January 2020.
This paper is concerned with the optimal stopping problem for Itô diffusion processes over a class of stopping times. Necessary and sufficient optimality conditions are studied for a parametrically specified class of stopping times. A detailed analysis is given for the case of one-dimensional diffusion processes and threshold stopping times. Necessary and sufficient conditions are put forward for optimality of a threshold stopping time over all stopping times. A number of relations are obtained between the solution of the optimal stopping problem over the class of threshold moments and the solution of the free-boundary problem.

中文翻译：

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扩散过程的阈值停止时间的最优性

概率理论及其应用，第65卷，第3期，第341-358页，2020年1月。
本文涉及一类停止时间内Itô扩散过程的最优停止问题。对于参数指定的停止时间类别，研究了必要和充分的最佳条件。对一维扩散过程和阈值停止时间的情况进行了详细分析。提出了在所有停止时间内优化阈值停止时间的必要和充分条件。在阈值矩类上的最佳停止问题的解与自由边界问题的解之间获得了许多关系。