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On the structure of general mean-variance hedging strategies

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  • Ale\v{s} \v{C}ern\'y
  • Jan Kallsen
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    Abstract

    We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure $P^{\star}$ which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to $P^{\star}$ coincides with the variance-optimal martingale measure relative to the original probability measure $P$.

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    File URL: http://arxiv.org/pdf/0708.1715
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0708.1715.

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    Date of creation: Aug 2007
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    Publication status: Published in Annals of Probability 2007, Vol. 35, No. 4, 1479-1531
    Handle: RePEc:arx:papers:0708.1715

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    Web page: http://arxiv.org/

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Jianming Xia & Jia-An Yan, 2006. "Markowitz'S Portfolio Optimization In An Incomplete Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 203-216.
    2. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    3. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
    4. Ales Čern� & Jan Kallsen, 2008. "Mean-Variance Hedging And Optimal Investment In Heston'S Model With Correlation," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 473-492.
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    Cited by:
    1. Mats Brod\'en & Peter Tankov, 2010. "Tracking errors from discrete hedging in exponential L\'evy models," Papers 1003.0709, arXiv.org.
    2. Mathieu Rosenbaum & Peter Tankov, 2011. "Asymptotically optimal discretization of hedging strategies with jumps," Papers 1108.5940, arXiv.org, revised Apr 2014.
    3. Liao Wang & Johannes Wissel, 2013. "Mean-variance hedging with oil futures," Finance and Stochastics, Springer, vol. 17(4), pages 641-683, October.
    4. Bruno R\'emillard & Sylvain Rubenthaler, 2012. "Optimal hedging in discrete time," Papers 1211.5035, arXiv.org.
    5. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
    6. Jan Kallsen & Johannes Muhle-Karbe & Richard Vierthauer, 2009. "Asymptotic Power Utility-Based Pricing and Hedging," Papers 0912.3362, arXiv.org, revised Jan 2013.
    7. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
    8. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org.

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