Optimal Stopping Rule for the No-Information Duration Problem with Random Horizon
Optimal Stopping Rule for the No-Information Duration Problem with Random Horizon
复制标题
随机时限无信息持续时间问题的最优停止规则
DOI：
10.1239/aap/1386857856
复制
发表时间：
2013
影响因子：
1.2
通讯作者：
M. Tamaki
中科院分区：
文献类型：
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作者：
M. Tamaki
作为秘书问题的一个版本，Ferguson，Hardwick和Tamaki（1992）考虑了一个称为持续时间问题的最优停止问题。基本持续时间问题是经典的持续时间问题，其目标是当已知数量的可排序对象以随机顺序出现时，最大化相对最佳对象的拥有时间。在本文中，我们推广这个经典的问题在两个方向上，允许数量N（可用对象）是一个随机变量与一个已知的上限n，也允许的对象出现根据伯努利试验。对于我们的随机时间跨度问题，根据规划时间跨度是N还是n，可以考虑两种模型。由于最优规则的形式一般是复杂的，我们主要关心的是给每个模型一个充分条件，使最优规则是简单的。对于N具有均匀分布、广义均匀分布或截尾几何分布，最优规则在所谓的秘书情况下被证明是简单的。当n → ∞时，也将给出这些先验的渐近结果。
As a version of the secretary problem, Ferguson, Hardwick and Tamaki (1992) considered an optimal stopping problem called the duration problem. The basic duration problem is the classical duration problem, in which the objective is to maximize the time of possession of a relatively best object when a known number of rankable objects appear in random order. In this paper we generalize this classical problem in two directions by allowing the number N (of available objects) to be a random variable with a known upper bound n and also allowing the objects to appear in accordance with Bernoulli trials. Two models can be considered for our random horizon duration problem according to whether the planning horizon is N or n. Since the form of the optimal rule is in general complicated, our main concern is to give to each model a sufficient condition for the optimal rule to be simple. For N having a uniform, generalized uniform, or curtailed geometric distribution, the optimal rule is shown to be simple in the so-called secretary case. The asymptotic results, as n → ∞, will also be given for these priors.