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Conditional Davis Pricing

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  • Kasper Larsen
  • Halil Mete Soner
  • Gordan v{Z}itkovi'c

Abstract

We study the set of marginal utility-based prices of a financial derivative in the case where the investor has a non-replicable random endowment. We provide an example showing that even in the simplest of settings - such as Samuelson's geometric Brownian motion model - the interval of marginal utility-based prices can be a non-trivial strict subinterval of the set of all no-arbitrage prices. This is in stark contrast to the case with a replicable endowment where non- uniqueness is exceptional. We provide formulas for the end points for these prices and illustrate the theory with several examples.

Suggested Citation

  • Kasper Larsen & Halil Mete Soner & Gordan v{Z}itkovi'c, 2017. "Conditional Davis Pricing," Papers 1702.02087, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1702.02087
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    References listed on IDEAS

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    1. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    2. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
    3. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    4. 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.
    5. Kasper Larsen & Halil Soner & Gordan Žitković, 2016. "Facelifting in utility maximization," Finance and Stochastics, Springer, vol. 20(1), pages 99-121, January.
    6. Gu, Lingqi & Lin, Yiqing & Yang, Junjian, 2016. "On the dual problem of utility maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1019-1035.
    7. Freddy Delbaen & Walter Schachermayer, 1998. "A Simple Counterexample to Several Problems in the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 1-11, January.
    8. Kasper Larsen & Gordan v{Z}itkovi'c, 2011. "On utility maximization under convex portfolio constraints," Papers 1102.0346, arXiv.org, revised Feb 2013.
    9. (**), 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.
    10. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
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