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.
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Jacka, S., Berkaoui, A. & Warren, J. No arbitrage and closure results for trading cones with transaction costs. Finance Stoch 12, 583–600 (2008). https://doi.org/10.1007/s00780-008-0075-7
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DOI: https://doi.org/10.1007/s00780-008-0075-7