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

Glover, K

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

Glover, K

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Publisher:: CAMBRIDGE UNIV PRESS
Publication Type:: Journal Article
Citation:: JOURNAL OF APPLIED PROBABILITY, 2022
Issue Date:: 2022-12-22

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Field	Value	Language
dc.contributor.author	Glover, K https://orcid.org/0000-0002-1518-3482
dc.date.accessioned	2023-03-12T22:14:47Z
dc.date.available	2023-03-12T22:14:47Z
dc.date.issued	2022-12-22
dc.identifier.citation	JOURNAL OF APPLIED PROBABILITY, 2022
dc.identifier.issn	0021-9002
dc.identifier.issn	1475-6072
dc.identifier.uri	http://hdl.handle.net/10453/167071
dc.description.abstract	<jats:title>Abstract</jats:title> <jats:p>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. However, the expected value upon stopping is lower due to the additional uncertainty present.</jats:p>
dc.language	English
dc.publisher	CAMBRIDGE UNIV PRESS
dc.relation.ispartof	JOURNAL OF APPLIED PROBABILITY
dc.relation.isbasedon	10.1017/jpr.2022.78
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.rights	This article has been published in a revised form in Journal of applied probability. https://doi.org/10.1017/jpr.2022.78. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © Copyright holder
dc.subject	0102 Applied Mathematics, 0104 Statistics
dc.subject.classification	Statistics & Probability
dc.title	With or without replacement? Sampling uncertainty in Shepp's urn scheme
dc.type	Journal Article
utslib.for	0102 Applied Mathematics
utslib.for	0104 Statistics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Finance Discipline
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access	*
utslib.copyright.embargo	2023-06-21T00:00:00+1000Z
dc.date.updated	2023-03-12T22:14:46Z
pubs.publication-status	Published

Abstract:

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. However, the expected value upon stopping is lower due to the additional uncertainty present.

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http://hdl.handle.net/10453/167071