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No-arbitrage criteria for financial markets with efficient friction

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Author Info

  • (**), Christophe Stricker

    ()
    (Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon, Cedex France)

  • (*), Miklós Rásonyi

    (Computer and Automation Institute of the Hungarian Academy of Sciences, 1111 Budapest, Hungary Manuscript)

  • Yuri Kabanov

    ()
    (Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon, Cedex France)

Abstract

We consider a multi-asset discrete-time model of a financial market with proportional transaction costs and efficient friction and prove necessary and sufficient conditions for the absence of arbitrage. Our main result is an extension of the Dalang-Morton-Willinger theorem. As an application, we establish a hedging theorem giving a description of the set of initial endowments which allows to super-replicate a given contingent claim.

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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 6 (2002)
Issue (Month): 3 ()
Pages: 371-382

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Handle: RePEc:spr:finsto:v:6:y:2002:i:3:p:371-382

Note: received: February 2001; final version received: September 2001
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Web page: http://www.springerlink.com/content/101164/

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Related research

Keywords: Transaction costs; arbitrage; hedging; solvency;

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Citations

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Cited by:
  1. Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 692-708, August.
  2. Emmanuel Denis & Yuri Kabanov, 2012. "Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs," Finance and Stochastics, Springer, vol. 16(1), pages 135-154, January.
  3. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
  4. 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.
  5. Przemys{\l}aw Rola, 2014. "Arbitrage in markets with bid-ask spreads," Papers 1407.3372, arXiv.org.
  6. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
  7. Tokarz, Krzysztof & Zastawniak, Tomasz, 2006. "American contingent claims under small proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 65-85, December.
  8. Bruno Bouchard & Huy\^en Pham, 2006. "Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns," Papers math/0602451, arXiv.org.
  9. Christoph Czichowsky & Johannes Muhle-Karbe & Walter Schachermayer, 2012. "Transaction Costs, Shadow Prices, and Duality in Discrete Time," Papers 1205.4643, arXiv.org, revised Jan 2014.
  10. Bruno Bouchard, 2005. "No-arbitrage in discrete-time markets with proportional transaction costs and general information structure," Papers math/0501045, arXiv.org.
  11. Dmitry B. Rokhlin, 2006. "Martingale selection problem and asset pricing in finite discrete time," Papers math/0602594, arXiv.org, revised Feb 2006.
  12. Peter Bank & Selim G\"okay, 2013. "Superreplication when trading at market indifference prices," Papers 1310.3113, arXiv.org.
  13. Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
  14. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
  15. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
  16. Dmitry B. Rokhlin, 2006. "Constructive no-arbitrage criterion under transaction costs in the case of finite discrete time," Papers math/0603284, arXiv.org.
  17. Teemu Pennanen & Irina Penner, 2008. "Hedging of claims with physical delivery under convex transaction costs," Papers 0810.2016, arXiv.org.

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