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Facelifting in utility maximization

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  • Kasper Larsen
  • Halil Soner
  • Gordan Žitković

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Kasper Larsen & Halil Soner & Gordan Žitković, 2016. "Facelifting in utility maximization," Finance and Stochastics, Springer, vol. 20(1), pages 99-121, January.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:1:p:99-121
    DOI: 10.1007/s00780-015-0274-y
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    References listed on IDEAS

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    1. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    2. Kasper Larsen & Gordan v{Z}itkovi'c, 2011. "On utility maximization under convex portfolio constraints," Papers 1102.0346, arXiv.org, revised Feb 2013.
    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. repec:dau:papers:123456789/1533 is not listed on IDEAS
    5. 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, April.
    6. 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.
    7. Jean-François Chassagneux & Romuald Elie & Idris Kharroubi, 2015. "When terminal facelift enforces delta constraints," Finance and Stochastics, Springer, vol. 19(2), pages 329-362, April.
    8. (**), 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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    Citations

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    Cited by:

    1. Kasper Larsen & Halil Mete Soner & Gordan v{Z}itkovi'c, 2017. "Conditional Davis Pricing," Papers 1702.02087, arXiv.org, revised Aug 2018.
    2. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    3. Kasper Larsen & Halil Mete Soner & Gordan Žitković, 2020. "Conditional Davis pricing," Finance and Stochastics, Springer, vol. 24(3), pages 565-599, July.
    4. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.
    5. Umut Cetin & Kasper Larsen, 2020. "Uniqueness in Cauchy problems for diffusive real-valued strict local martingales," Papers 2007.15041, arXiv.org, revised May 2022.

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    More about this item

    Keywords

    Boundary layer; Convex analysis; Convex duality; Facelift; Financial mathematics; Incomplete markets; Markov processes; Utility maximization; Unspanned endowment; 91G10; 91G80; 60K35; C61; G11;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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