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- Title
No arbitrage and closure results for trading cones with transaction costs.
- Authors
Jacka, Saul; Berkaoui, Abdelkarem; Warren, Jon
- Abstract
In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, ). 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.
- Subjects
PROGRAM trading (Securities); STOCK exchanges; SWAPS (Finance); ARBITRAGE; FINANCE; CURRENCY swaps; DEBT exchanges; COMMODITY exchanges; FUTURES market
- Publication
Finance & Stochastics, 2008, Vol 12, Issue 4, p583
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-008-0075-7