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Robust Hedging with Proportional Transaction Costs

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  • Yan Dolinsky
  • H. Mete Soner
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    Abstract

    Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Both the stock and the option trading is subject to proportional transaction costs. The main theorem is duality between hedging and a Monge-Kantorovich type optimization problem. In this dual transport problem the optimization is over all the probability measures which satisfy an approximate martingale condition related to consistent price systems in addition to the usual marginal constraints.

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    File URL: http://arxiv.org/pdf/1302.0590
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1302.0590.

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    Date of creation: Feb 2013
    Date of revision: Aug 2013
    Handle: RePEc:arx:papers:1302.0590

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    1. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, Springer, vol. 14(2), pages 179-207, April.
    2. Alexander Cox & Jan Obłój, 2011. "Robust pricing and hedging of double no-touch options," Finance and Stochastics, Springer, Springer, vol. 15(3), pages 573-605, September.
    3. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, Springer, vol. 2(4), pages 329-347.
    4. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 11(3), pages 285-314.
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    Cited by:
    1. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and Duality in Nondominated Discrete-Time Models," Papers 1305.6008, arXiv.org, revised Feb 2014.

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