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Facelifting in Utility Maximization

  • Kasper Larsen
  • H. Mete Soner
  • Gordan Zitkovic
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    We establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility-maximization in incomplete semimartingale-driven financial markets. Unlike in the lower- and upper-hedging problems, and somewhat unexpectedly, a facelift turns out to exist in utility-maximization despite strict convexity in the objective function. In addition to discussing our results in their natural, Markovian environment, we also use them to show that the dual optimizer cannot be found in the set of countably-additive (martingale) measures in a wide variety of situations.

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    File URL: http://arxiv.org/pdf/1404.2227
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    Paper provided by arXiv.org in its series Papers with number 1404.2227.

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    Date of creation: Apr 2014
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    Handle: RePEc:arx:papers:1404.2227
    Contact details of provider: Web page: http://arxiv.org/

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    1. Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility-Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 203-212.
    2. Uwe Wystup & Uwe Schmock & Steven E. Shreve, 2002. "Valuation of exotic options under shortselling constraints," Finance and Stochastics, Springer, vol. 6(2), pages 143-172.
    3. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    4. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
    5. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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