Finance and Stochastics

, Volume 12, Issue 4, pp 583–600

No arbitrage and closure results for trading cones with transaction costs


DOI: 10.1007/s00780-008-0075-7

Cite this article as:
Jacka, S., Berkaoui, A. & Warren, J. Finance Stoch (2008) 12: 583. doi:10.1007/s00780-008-0075-7


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.


Arbitrage Proportional transaction costs Fundamental theorem of asset pricing Convex cone 

Mathematics Subject Classification (2000)

91B24 91B28 52A20 60H30 

JEL Classification

G10 G11 G13 

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of WarwickCoventryUK
  2. 2.College of SciencesAl-Imam Mohammed Ibn Saud Islamic UniversityRiyadhSaudi Arabia

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