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No-arbitrage of second kind in countable markets with proportional transaction costs

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  • Bruno Bouchard
  • Erik Taflin

Abstract

Motivated by applications to bond markets, we propose a multivariate framework for discrete time financial markets with proportional transaction costs and a countable infinite number of tradable assets. We show that the no-arbitrage of second kind property (NA2 in short), recently introduced by Rasonyi for finite-dimensional markets, allows us to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition. We also extend to this context the equivalence between NA2 and the existence of many (strictly) consistent price systems.

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  • Bruno Bouchard & Erik Taflin, 2010. "No-arbitrage of second kind in countable markets with proportional transaction costs," Papers 1008.3276, arXiv.org, revised Feb 2013.
    • Handle: RePEc:arx:papers:1008.3276
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    References listed on IDEAS

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    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. 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.
    3. Dimitri de Vallière & Emmanuel Denis & Yuri Kabanov, 2009. "Hedging of American options under transaction costs," Post-Print hal-00488157, HAL.
    4. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
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    Cited by:

    1. Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.
    2. Kabanov, Yuri & Lépinette, Emmanuel, 2013. "Essential supremum and essential maximum with respect to random preference relations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 488-495.
    3. Kabanov, Yuri & Lépinette, Emmanuel, 2013. "Essential supremum with respect to a random partial order," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 478-487.

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