For a price process that has an equivalent risk neutral measure, we investigate if the same property holds when the numéraire is changed. We give necessary and sufficient conditions under which the price process of a particular asset — which should be thought of as a different currency — can be chosen as new numéraire. The result is related to the characterisation of attainable claims that can be hedged. Roughly speaking: the asset representing the new currency is a reasonable investment (in terms of the old currency) if and only if the market does not permit arbitrage opportunities in terms of the new currency as numéraire. This rough but economically meaningful idea is given a precise content in this paper. The main ingredients are a duality relation as well as a result on maximal elements. The paper also generalises results previously obtained by Jacka, Ansel-Stricker and the authors.
Mathematics Subject Classification (2000)
JEL Classification
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Delbaen, F., Schachermayer, W. (2006). The No-Arbitrage Property under a Change of Numéraire (1995). In: The Mathematics of Arbitrage. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31299-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-31299-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21992-7
Online ISBN: 978-3-540-31299-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)