论文标题
最佳停止随机运输最小化临床代理成本
Optimal Stopping of Stochastic Transport Minimizing Submartingale Costs
论文作者
论文摘要
给定一个随机状态过程$（x_t）_t $和一个实价的字体制品成本过程$（s_t）_t $，我们表征了最佳停止时间$τ$，从而最大程度地减少了$s_τ$的期望，而在给定的初始和目标分布$ $ $和$μ$和$ n $ n和$ x_0 $ x_ $ sim和sim sim和sim sim和sim sim和sim sim和sim sim sim和sim sim和sim sim和sim x $ sim和sim sim和x n $ sim和x $ x $和x $ x $ n。考虑了双重优化问题，并证明在适当的条件下已达到。然后，双重问题的最佳解决方案提供了一个触点集，该联系人表征了最佳停止的位置。最佳停止时间是唯一确定的，因为我们在对$（x_t，s_t）_t $上假定自然结构假设的第一个打击时间，这将最佳运输理论的成本概括为扭曲条件。本文扩展了[15，16]研究的布朗动议设置，并处理了更多的一般成本。
Given a stochastic state process $(X_t)_t$ and a real-valued submartingale cost process $(S_t)_t$, we characterize optimal stopping times $τ$ that minimize the expectation of $S_τ$ while realizing given initial and target distributions $μ$ and $ν$, i.e., $X_0\sim μ$ and $X_τ\sim ν$. A dual optimization problem is considered and shown to be attained under suitable conditions. The optimal solution of the dual problem then provides a contact set, which characterizes the location where optimal stopping can occur. The optimal stopping time is uniquely determined as the first hitting time of this contact set provided we assume a natural structural assumption on the pair $(X_t, S_t)_t$, which generalizes the twist condition on the cost in optimal transport theory. This paper extends the Brownian motion settings studied in [15, 16] and deals with more general costs.
