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Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs

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  • Bouchard, Bruno
  • Touzi, Nizar
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    Abstract

    We consider a multivariate financial market with transaction costs as in Kabanov. We study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. We prove that the value of this stochastic control problem is given by the cost of the cheapest buy-and-hold strategy. This is an extension of the already known result in the one-dimensional case. An important feature of our analysis is that we do not make use of the dual formulation of the problem, as in the previous literature.

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    File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/1533/2/2000-5.ps
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    Bibliographic Info

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/1533.

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    Date of creation: 2000
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    Publication status: Published in Annals of Applied Probability, 2000, Vol. 10, no. 3. pp. 685-708.Length: 23 pages
    Handle: RePEc:dau:papers:123456789/1533

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    Related research

    Keywords: viscosity solutions; dynamic programming; hedging options; Transaction costs;

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    Cited by:
    1. Campi, Luciano & Schachermayer, Walter, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/5455, Paris Dauphine University.
    2. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print, HAL halshs-00703138, HAL.
    3. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org, revised Sep 2014.
    4. Bruno Bouchard, 2005. "No-arbitrage in discrete-time markets with proportional transaction costs and general information structure," Papers math/0501045, arXiv.org.
    5. Bouchard, Bruno, 2002. "Stochastic targets with mixed diffusion processes and viscosity solutions," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 101(2), pages 273-302, October.
    6. Bruno Bouchard & Ngoc-Minh Dang, 2013. "Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation," Finance and Stochastics, Springer, Springer, vol. 17(1), pages 31-72, January.
    7. Bentahar, Imen & Bouchard, Bruno, 2007. "Explicit characterization of the super-replication strategy in financial markets with partial transaction costs," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 117(5), pages 655-672, May.
    8. 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.

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