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Explicit characterization of the super-replication strategy in financial markets with partial transaction costs

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  • Imen Bentahar
  • Bruno Bouchard
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    Abstract

    We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi (2000) except that some of the assets can be exchanged freely, i.e. without paying transaction costs. This is the so-called non-effcient friction case. To our knowledge, this is the first time that such a model is considered in a continuous time setting. In this context, we generalize the result of the above paper and prove that the super-replication price is given by the cost of the cheapest hedging strategy in which the number of non-freely exchangeable assets is kept constant over time.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2005-053.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-053.

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    Length: 36 pages
    Date of creation: Oct 2005
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    Handle: RePEc:hum:wpaper:sfb649dp2005-053

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    Keywords: Transaction costs; hedging options; viscosity solutions;

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    1. Nizar Touzi, 1999. "Super-replication under proportional transaction costs: From discrete to continuous-time models," Computational Statistics, Springer, vol. 50(2), pages 297-320, October.
    2. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165.
    3. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    4. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    5. repec:fth:inseep:9513 is not listed on IDEAS
    6. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
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