We study optimal stopping of strong Markov processes under random implementation delay. By random implementation delay we mean the following: the payoff is not realised immediately when the process is stopped but rather after a random waiting period. The distribution of the random waiting period is assumed to be phase-type. We prove first a general result on the solvability of the problem. Then we study the case of Coxian distribution both in general and with scalar diffusion dynamics in more detail. The study is concluded with two explicit examples.

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关于相位型分布实现延迟下最优停止的一些结果

我们研究了在随机执行延迟下强马尔可夫过程的最优停止。随机执行延迟指的是：收益不会在流程停止时立即实现，而是在随机等待期之后实现。假定随机等待时间段的分布是相位型的。我们首先证明问题的可解决性是一个一般结果。然后，我们将研究一般情况下的Coxian分布情况以及具有标量扩散动力学的情况。本研究以两个明确的例子结束。