No arbitrage and closure results for trading cones with transaction costs

@article{Jacka2008NoAA,
title={No arbitrage and closure results for trading cones with transaction costs},
author={Saul Jacka and Abdelkarem Berkaoui and Jon Warren},
journal={Finance and Stochastics},
year={2008},
volume={12},
pages={583-600}
}

In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper of 2004. 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, Ã, does obey the Fundamental Theorem of Asset Pricing and secondly, if Ã is arbitrage-free then it is the closure of A. We… CONTINUE READING