Optimal stopping of independent random variables and maximizing prophets
type: Item
instance of: scholarly article
title: Optimal stopping of independent random variables and maximizing prophets
zbMATH Open document ID: 0563.60044
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: The prophet inequality for a sequence of independent nonnegative random variables shows that the ratio of the mean of the maximum of the sequence to the optimal expected return using stopping times is always bounded by 2; i.e., on average, the proportional advantage of a prophet with complete foresight over a gambler using nonanticipating stopping rules is at most 2. Here, an inequality linking the mean of the sum of the k largest order statistics of the sequence and the optimal expected return is derived. This implies that if the k largest order statistics are close to the maximum in mean then the proportional advantage of the prophet is at most of order \((k+1)/k\). An extension of the additive prophet inequality for uniformly bounded independent random variables is also given.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62L15
zbMATH DE Number: 3897940
zbMATH Keywords: prophet inequality
zbMATH Keywords: optimal expected return
zbMATH Keywords: stopping rules
zbMATH Keywords: order statistics
author: D. P. Kennedy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993009
OpenAlex ID: W2086057661
DOI: 10.1214/AOP/1176993009
description: scientific article; zbMATH DE number 3897940