In discrete time a local martingale is a martingale under an equivalent probability measure
type: Item
instance of: scholarly article
title: In discrete time a local martingale is a martingale under an equivalent probability measure
zbMATH Open document ID: 1164.60031
published in: Finance and Stochastics
publication date: 2009-02-28T00:00:00Z
review text: The author formulates and proves the following result. Let a discrete-time infinite horizon model with an adapted \(d\)-dimensional process \(S\) be considered. If \(S\) is a local martingale on some stochastic basis, then there exists an equivalent probability measure under which \(S\) is a martingale with respect to the same filtration. The proof uses an approach originating from geometric functional analysis. It is based on separation arguments in an ingeniously chosen countably-normed space where the separating functional happens to be the density of the desired martingale measure. The most involved part of the proof is to verify the conditions of the Krein-Šchmulian theorem.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 5520646
zbMATH Keywords: martingale
zbMATH Keywords: generalized martingale
zbMATH Keywords: Dalang-Morton-Willinger theorem
zbMATH Keywords: Krein-Šmulian theorem
zbMATH Keywords: free lunch
author: Yuri Kabanov
MaRDI profile type: Publication
full work available at URL: s00780-008-0063-y
OpenAlex ID: W2013937202
cites work: Equivalent martingale measures and no-arbitrage in stochastic securities market models
cites work: Local martingales and the fundamental asset pricing theorems in the discrete-time case
cites work: Q4788298
cites work: Q2725602
cites work: MARTINGALE MEASURES FOR DISCRETE‐TIME PROCESSES WITH INFINITE HORIZON
DOI: 10.1007/S00780-008-0063-Y
description: scientific article; zbMATH DE number 5520646