A general approximation method for optimal stopping and random delay
针对无限时域连续时间最优停时问题，提出一种连续时间马尔可夫链近似方法，适用于一般奖励函数和基础过程，并扩展到随机延迟情形，给出误差上界和高效两阶段实现方案。
Abstract This study examines the continuous‐time optimal stopping problem with an infinite horizon under Markov processes. Existing research focuses on finding explicit solutions under certain assumptions of the reward function or underlying process; however, these assumptions may either not be fulfilled or be difficult to validate in practice. We developed a continuous‐time Markov chain (CTMC) approximation method to find the optimal solution, which applies to general reward functions and underlying Markov processes. We demonstrated that our method can be used to solve the optimal stopping problem with a random delay, in which the delay could be either an independent random variable or a function of the underlying process. We established a theoretical upper bound for the approximation error to facilitate error control. Furthermore, we designed a two‐stage scheme to implement our method efficiently. The numerical results show that the proposed method is accurate and rapid under various model specifications.