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

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  • Saul Jacka
  • Abdelkarem Berkaoui
  • Jon Warren
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    Abstract

    The paper considers trading with proportional transaction costs. We give a necessary and sufficient condition for A, the cone of claims attainable from zero endowment, to be closed, and show, in general, how to represent its closure in such a way that it is the cone of claims attainable for zero endowment, for a different set of trading prices. The new representation obeys the Fundamental Theorem of Asset Pricing. We then show how to represent claims and in a final section show how any such setup corresponds to a coherent risk measure.

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    File URL: http://arxiv.org/pdf/math/0602178
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0602178.

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    Date of creation: Feb 2006
    Date of revision: Apr 2008
    Handle: RePEc:arx:papers:math/0602178

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    Web page: http://arxiv.org/

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    1. (**), Christophe Stricker & (*), Miklós Rásonyi & Yuri Kabanov, 2002. "No-arbitrage criteria for financial markets with efficient friction," Finance and Stochastics, Springer, vol. 6(3), pages 371-382.
    2. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    3. D. Vallière & E. Denis & Y. Kabanov, 2009. "Hedging of American options under transaction costs," Finance and Stochastics, Springer, vol. 13(1), pages 105-119, January.
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