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## No arbitrage and closure results for trading cones with transaction costs

### 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

Topics: HB, QA
Publisher: Springer
Year: 2008
OAI identifier: oai:wrap.warwick.ac.uk:2493

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