Stop rule and supremum expectations of i.i.d. random variables: A complete comparison by conjugate duality
type: Item
instance of: scholarly article
title: Stop rule and supremum expectations of i.i.d. random variables: A complete comparison by conjugate duality
zbMATH Open document ID: 0598.60044
DOI: 10.1016/0047-259X(86)90095-3
author: Robert P. Kertz
published in: Journal of Multivariate Analysis
publication date: 1986-01-01T00:00:00Z
review text: \(X_ 1,...,X_ n\) are independent and identically distributed random variables taking values in the closed interval [0,1]. Define \(V(X_ 1,...,X_ n)\) as \(\sup \{EX_ t:\) t is a stop rule for \(X_ 1,...,X_ n\}\). For x in the closed interval [0,1], a nonnegative strictly increasing strictly concave function \(G_ n(x)\) is constructed such that the set of ordered pairs \(\{(x,y):\) \(x=V(X_ 1,...,X_ n)\) and \(y=E(\max_{j\leq n}X_ j)\) for some \(X_ 1,...,X_ n\}\) is precisely the set \(\{(x,y):\) \(x\leq y\leq G_ n(x)\); \(0\leq x\leq 1\}\). Various inequalities are derived from this result.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 90C99
zbMATH DE Number: 3965100
zbMATH Keywords: optimal stopping
zbMATH Keywords: extremal distributions
zbMATH Keywords: inequalities for stochastic processes
zbMATH Keywords: conjugate duality
zbMATH Keywords: Young's inequality
reviewed by: Lionel Weiss
MaRDI profile type: Publication
cites work: Q4167627
cites work: Q5641856
cites work: Q4114551
cites work: Q5533446
cites work: Q4121644
cites work: Prophet Inequalities and Order Selection in Optimal Stopping Problems
cites work: Ratio comparisons of supremum and stop rule expectations
cites work: Additive Comparisons of Stop Rule and Supremum Expectations of Uniformly Bounded Independent Random Variables
cites work: Comparisons of stop rule and supremum expectations of i.i.d. random variables
cites work: Stop Rule Inequalities for Uniformly Bounded Sequences of Random Variables
cites work: Semiamarts and finite values
cites work: Q5566063
cites work: Analytic Inequalities
cites work: Q5603731
cites work: Q5794747
description: scientific article; zbMATH DE number 3965100