Prophet-type inequalities for multi-choice optimal stopping
type: Item
instance of: scholarly article
title: Prophet-type inequalities for multi-choice optimal stopping
zbMATH Open document ID: 0621.60054
DOI: 10.1016/0304-4149(87)90029-9
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,..\). be independent random variables taking values in [0,1], and let \(v_ r=\sup E(X_{\tau_ 1}+X_{\tau_ 2}+...+X_{\tau_ r})\), where the supremum extends over all stopping times \(\tau_ 1<\tau_ 2<...<\tau_ r\). The author proves inequalities of the form E(sup \(X_ n)\leq F_ r(v_ r).\) He gives an explicit formula for the best possible function \(F_ r\). He also derives best possible constants \(1\leq C_ r\leq 2\) with E(sup \(X_ n)\leq C_ rv_ r\). It is known that \(C_ 1=2\). The constants \(C_ r\) decrease and tend to one rapidly. E.g. \(C_ 2=1.1716\).
reviewed by: Ulrich Krengel
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 4007366
zbMATH Keywords: prophet inequality
zbMATH Keywords: multiple optimal stopping
author: D. P. Kennedy
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90029-9
OpenAlex ID: W2024334917
cites work: Prophet Inequalities and Order Selection in Optimal Stopping Problems
cites work: Ratio comparisons of supremum and stop rule expectations
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cites work: Comparisons of stop rule and supremum expectations of i.i.d. random variables
cites work: Optimal stopping of independent random variables and maximizing prophets
cites work: Comparison of optimal value and constrained maxima expectations for independent random variables
cites work: Semiamarts and finite values
cites work: Note on Shift-Invariant Sets
Wikidata QID: Q127658275
description: scientific article; zbMATH DE number 4007366