With or without replacement? Sampling uncertainty in Shepp's urn scheme

2019/11/27 by Kristoffer Glover, Glover, Kristoffer · 1 citation
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Bandit Algorithms Research #FOS: Economics and business #FOS: Mathematics #Machine Learning and Algorithms #Probability (math.PR) #Statistical Finance (q-fin.ST) #math.PR #q-fin.ST

paper · pdf · doi:10.48550/arxiv.1911.11971

14 pages, 3 figures

openalex publication_date 2019/11/27 · arxiv created 2022/03/04 · arxiv updated 2022/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a variant of Shepp's classical urn problem in which the optimal stopper does not know whether sampling from the urn is done with or without replacement. By considering the problem's continuous-time analog, we provide bounds on the value function and in the case of a balanced urn (with an equal number of each ball type) an explicit solution is found. Surprisingly, the optimal strategy for the balanced urn is the same as in the classical urn problem.

Cited by

• On the optimal stopping of Gauss-Markov bridges with random pinning points

Related

• On Sampling without replacement and OK-Corral urn models
• Preferential Attachment When Stable
• Urn models with two types of strategies
• The Probability Distribution for Draws Until First Success Without Replacement
• Urns with simultaneous drawing