The paper deals with an optimal stopping problem for one-dimensional Ito diffusion process and terminal payoff function. We study the following problem: under what conditions the stopping time which is optimal over the class of threshold strategies (specifying by first time when the underlying process exceeds some level) remains optimal over all stopping times. We prove that excessiveness of payoff function is the only necessary and sufficient condition which connects optimality over the class of threshold stopping times and over all stopping times.

中文翻译：

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关于 Ito 扩散的最佳阈值停止时间

研究一维Ito扩散过程和终端收益函数的最优停止问题。我们研究以下问题：在什么条件下，对于阈值策略类别（当底层过程超过某个水平时第一次指定）最优的停止时间在所有停止时间上保持最优。我们证明了支付函数的过度性是连接阈值停止时间类和所有停止时间的最优性的唯一必要和充分条件。