Iterated conditional expectations
type: Item
instance of: scholarly article
title: Iterated conditional expectations
zbMATH Open document ID: 1197.60002
author: J. Quinn
author: Alexander Y. Gordon
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-05-10T00:00:00Z
review text: The paper discusses two results of \textit{A. S. Cherny} and \textit{P. G. Grigoriev} [Finance Stoch. 11, No. 2, 291--298 (2007; Zbl 1144.91008)]. The first one is general and concerns the distance between arbitrary equidistributed bounded random variables on a nonatomic probability space. The second one is a consequence of the first one and establishes a law invariance theorem for \(L^{\infty}\) dilatation monotone maps (in the nonatomic setting). The authors give a straightforward analytic proof of the second result. This proof is motivated by a simple geometric idea. Then it is shown that the first result is implied by the second one. It is emphasized that both the theorems, when properly interpreted physically, have many counterintuitive consequences, not only in coherent risk theory, as in [Zbl 1144.91008].
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 60A99
zbMATH DE Number: 5706236
zbMATH Keywords: Nonatomic probability space
zbMATH Keywords: equidistributed functions
zbMATH Keywords: conditional expectation
zbMATH Keywords: law invariance theorem
zbMATH Keywords: dilatation monotone map
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.02.001
OpenAlex ID: W1973823558
cites work: Dilatation monotone risk measures are law invariant
DOI: 10.1016/J.JMAA.2010.02.001
description: scientific article; zbMATH DE number 5706236