In a classical, continuous-time, optimal stopping problem, the agent chooses the best time to stop a stochastic process in order to maximise the expected discounted return. The agent can choose when to stop, and if at any moment they decide to stop, stopping occurs immediately with probability one. However, in many settings this is an idealistic oversimplification. Following Strack and Viefers we consider a modification of the problem in which stopping occurs at a rate which depends on the relative values of stopping and continuing: there are several different solutions depending on how the value of continuing is calculated. Initially we consider the case where stopping opportunities are constrained to be event times of an independent Poisson process. Motivated by the limiting case as the rate of the Poisson process increases to infinity, we also propose a continuous-time formulation of the problem where stopping can occur at any instant.

中文翻译：

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停止问题的随机规则

在经典的连续时间最优停止问题中，代理选择停止随机过程的最佳时间以最大化预期的贴现回报。代理可以选择何时停止，如果在任何时候他们决定停止，停止以概率 1 立即发生。然而，在许多情况下，这是一种理想主义的过度简化。在 Strack 和 Viefers 之后，我们考虑对问题进行修改，其中停止以取决于停止和继续的相对值的速率发生：根据如何计算继续的值，有几种不同的解决方案。最初，我们考虑停止机会被限制为独立泊松过程的事件时间的情况。随着泊松过程的速率增加到无穷大，受极限情况的推动，