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Paper No. 07-10

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S Jacka, A Berkaoui and J Warren

No Arbitrage and Closure Results for Trading Cones with Transaction Costs

Date: August 2007

Abstract: In this paper, we consider trading with proportional transaction costs as in [11]. We give a necessary and sufficient condition for 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, ˜ A, does obey the Fundamental Theorem of Asset Pricing and secondly, if ˜ A is arbitrage-free then it is the closure of A. We then conclude by showing how to represent claims.