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A Counterexample Concerning The Variance‐Optimal Martingale Measure

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  • Aleš Černý
  • Jan Kallsen

Abstract

The present note addresses an open question concerning a sufficient characterization of the variance‐optimal martingale measure. Denote by S the discounted price process of an asset and suppose that Q★ is an equivalent martingale measure whose density is a multiple of 1 −ϕ·ST for some S‐integrable process ϕ. We show that Q★ does not necessarily coincide with the variance‐optimal martingale measure, not even if ϕ·S is a uniformly integrable Q★‐martingale.

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  • Aleš Černý & Jan Kallsen, 2008. "A Counterexample Concerning The Variance‐Optimal Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 305-316, April.
    • Handle: RePEc:bla:mathfi:v:18:y:2008:i:2:p:305-316
    DOI: 10.1111/j.1467-9965.2007.00334.x
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    1. Aleš Černý & 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, July.
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    Cited by:

    1. Küchler Uwe & Tappe Stefan, 2009. "Option pricing in bilateral Gamma stock models," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 281-307, December.
    2. 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.
    3. Aleš Černý & 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, July.
    4. Uwe Kuchler & Stefan Tappe, 2019. "Option pricing in bilateral Gamma stock models," Papers 1907.09862, 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.

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