发表机构
Bunkyo Gakuin University（文京学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出有限时域离散时间多重停止理论，区分一般递归动态规划与单调结构，构造最优停止时间向量，并应用于多重选择最后成功问题，给出下界证明及阈值常数。
AI 中文摘要
当停止区域在后续转移下保持不变时，最优停止问题称为单调的，此时一步前瞻停止时间是最优的。我们发展了一个有限时域离散时间的多重停止理论，该理论将一般递归动态规划与这种更强的单调结构区分开来。通过扩展经典的鞅系统方法，我们在不假设单调性的情况下构造了一个递归定义的最优停止时间向量。如果单调性在每个执行水平上都成立，则该向量与一步前瞻停止时间的递归向量一致。一个有界反例表明，仅原始单停止问题的单调性是不够的，而当水平一的一步前瞻函数是确定性的时，单调性会传播到每个水平。我们将该理论应用于多重选择最后成功问题。对于经典的独立赔率设置，连续时间泊松嵌入给出了多重停止下界的另一种证明，并阐明了相关的阈值常数。我们还考察了随机视界、马尔可夫依赖试验以及未知成功概率的情况。
英文摘要
An optimal stopping problem is monotone when its stopping region is preserved under subsequent transitions, so that the one-step look-ahead stopping time is optimal. We develop a finite-horizon discrete-time theory of multiple stopping that separates general recursive dynamic programming from this stronger monotone structure. Extending the classical martingale-system approach, we construct a recursively defined optimal vector of stopping times without assuming monotonicity. If monotonicity holds at every exercise level, this vector coincides with the recursive vector of one-step look-ahead stopping times. A bounded counterexample shows that monotonicity of the original single-stopping problem alone is insufficient, whereas monotonicity propagates to every level when the level-one one-step look-ahead function is deterministic. We apply the theory to multiple-selection last-success problems. For the classical independent odds setting, a continuous-time Poisson embedding gives an alternative proof of the multiple-stopping lower bound and clarifies the associated threshold constants. We also examine random horizons, Markov-dependent trials, and an unknown success probability
Comments55 pages, 1 figure
