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Hedging of claims with physical delivery under convex transaction costs

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  • Teemu Pennanen
  • Irina Penner

Abstract

We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer's robust no arbitrage condition implies that the set of claims hedgeable with zero cost is closed in probability. Combined with classical techniques of convex analysis, the closedness yields a dual characterization of premium processes that are sufficient to superhedge a given claim process. We also extend the fundamental theorem of asset pricing for general conical models.

Suggested Citation

  • Teemu Pennanen & Irina Penner, 2008. "Hedging of claims with physical delivery under convex transaction costs," Papers 0810.2016, arXiv.org.
    • Handle: RePEc:arx:papers:0810.2016
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    References listed on IDEAS

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    1. (**), 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.
    2. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    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. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.

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