具有无界报酬的无折扣最优停止
Undiscounted optimal stopping with unbounded rewards
摘要：
我们研究最优停止的Feller-Markov过程，以最大限度地提高一个未贴现的功能，包括运行和终端奖励。在有限时间范围内，我们将经典的结果扩展到无界奖励。在无限视界中，我们求助于底层过程的遍历结构。当跑步奖励是轻微的惩罚延迟停止（即，它在不变测度下的期望是负的），我们证明了最优停时的存在性，并以标准式的形式给出了最优停时为第一次进入闭集的时间.本文通过放松奖励的有界性来推广Palczewski，Stettner（2014），Stoch Proc Appl 124（12）3887-3920。
英文摘要：
We study optimal stopping of Feller-Markov processes to maximise an undiscounted functional consisting of running and terminal rewards. In a finite-time horizon setting, we extend classical results to unbounded rewards. In infinite horizon, we resort to ergodic structure of the underlying process. When the running reward is mildly penalising for delaying stopping (i.e., its expectation under the invariant measure is negative), we show that an optimal stopping time exists and is given in a standard form as the time of first entrance to a closed set. This paper generalises Palczewski, Stettner (2014), Stoch Proc Appl 124(12) 3887-3920, by relaxing boundedness of rewards.
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