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

Author

Listed:
  • Saul Jacka
  • Abdelkarem Berkaoui
  • Jon Warren

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.

Suggested Citation

  • Saul Jacka & Abdelkarem Berkaoui & Jon Warren, 2006. "No-arbitrage and closure results for trading cones with transaction costs," Papers math/0602178, arXiv.org, revised Apr 2008.
    • Handle: RePEc:arx:papers:math/0602178
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    References listed on IDEAS

    as
    1. 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.
    2. (**), 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.
    3. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
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    Cited by:

    1. Saul Jacka & Seb Armstrong & Abdel Berkaoui, 2017. "Multi-currency reserving for coherent risk measures," Papers 1712.01319, arXiv.org, revised Dec 2017.
    2. Christoph Kühn & Alexander Molitor, 2019. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 23(4), pages 1049-1077, October.
    3. Tomasz R. Bielecki & Igor Cialenco & Rodrigo Rodriguez, 2012. "No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs," Papers 1205.6254, arXiv.org, revised Jun 2013.
    4. Christoph Kuhn & Alexander Molitor, 2018. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Papers 1811.11621, arXiv.org, revised Apr 2019.

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