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No arbitrage and closure results for trading cones with transaction costs

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Jacka, Saul D., Berkaoui, Abdelkarem and Warren, Jon. (2008) No arbitrage and closure results for trading cones with transaction costs. Finance and Stochastics, Vol.12 (No.4). pp. 583-600. ISSN 0949-2984

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Official URL: http://dx.doi.org/10.1007/s00780-008-0075-7

Abstract

In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for ${\mathcal{A}}$ , the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment, ${\tilde{ {\mathcal{A}}}}$ , does obey the fundamental theorem of asset pricing and, secondly, if ${\tilde{ {\mathcal{A}}}}$ is arbitrage-free then it is the closure of ${\mathcal{A}}$ . We then conclude by showing how to represent claims.

Item Type:	Journal Article
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Arbitrage -- Mathematical models, Transaction costs -- Mathematical models, Assets (Accounting), Convex functions, Cones (Operator theory)
Journal or Publication Title:	Finance and Stochastics
Publisher:	Springer
ISSN:	0949-2984
Date:	October 2008
Volume:	Vol.12
Number:	No.4
Page Range:	pp. 583-600
Identification Number:	10.1007/s00780-008-0075-7
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	[1] P. Artzner, F. Delbaen, J.-M. Eber and D. Heath (1999): Coherent measures of risk, Math. Finance 9(3), 203
URI:	http://wrap.warwick.ac.uk/id/eprint/2493