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Convex duality with transaction costs

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  • Yan Dolinsky
  • H. Mete Soner

Abstract

Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic hedging with the underlying stock, are allowed. The first one the problems considered is the model--independent hedging that requires the super--replication to hold for every continuous path. In the second one the market model is given through a probability measure P and the inequalities are understood P almost surely. The main result, using the convex duality, proves that the two super--replication problems have the same value provided that P satisfies the conditional full support property. Hence, the transaction costs prevents one from using the structure of a specific model to reduce the super--replication cost.

Suggested Citation

  • Yan Dolinsky & H. Mete Soner, 2015. "Convex duality with transaction costs," Papers 1502.01735, arXiv.org, revised Oct 2015.
    • Handle: RePEc:arx:papers:1502.01735
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    References listed on IDEAS

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    1. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    2. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    3. Walter Schachermayer, 2014. "The super-replication theorem under proportional transaction costs revisited," Papers 1405.1266, arXiv.org.
    4. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    5. Yan Dolinsky & Halil Mete Soner, 2013. "Martingale Optimal Transport and Robust Hedging in Continuous Time," Swiss Finance Institute Research Paper Series 13-13, Swiss Finance Institute.
    6. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
    7. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    8. repec:dau:papers:123456789/1533 is not listed on IDEAS
    9. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    10. Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.
    11. Yan DOLINSKY & Mete SONER, 2014. "Martingale Optimal Transport in the Skorokhod Space," Swiss Finance Institute Research Paper Series 14-62, Swiss Finance Institute.
    12. Erhan Bayraktar & Yuchong Zhang, 2013. "Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty," Papers 1309.1420, arXiv.org, revised Aug 2015.
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    Cited by:

    1. Matteo Burzoni, 2015. "Arbitrage and Hedging in model-independent markets with frictions," Papers 1512.01488, arXiv.org, revised Aug 2016.
    2. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.

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