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Derivative pricing based on local utility maximization


  • Jan Kallsen

    () (Institut für Mathematische Stochastik, Universität Freiburg, Eckerstraße 1, 79104 Freiburg i. Br., Germany Manuscript)


This paper discusses a new approach to contingent claim valuation in general incomplete market models. We determine the neutral derivative price which occurs if investors maximize their local utility and if derivative demand and supply are balanced. We also introduce the sensitivity process of a contingent claim. This process quantifies the reliability of the neutral derivative price and it can be used to construct price bounds. Moreover, it allows to calibrate market models in order to be consistent with initially observed derivative quotations.

Suggested Citation

  • Jan Kallsen, 2002. "Derivative pricing based on local utility maximization," Finance and Stochastics, Springer, vol. 6(1), pages 115-140.
  • Handle: RePEc:spr:finsto:v:6:y:2002:i:1:p:115-140
    Note: received: October 2000; final version received: February 2001

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    References listed on IDEAS

    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    2. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
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    Cited by:

    1. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672,, revised Mar 2018.
    2. Ibrahim Ekren & Ren Liu & Johannes Muhle-Karbe, 2015. "Optimal Rebalancing Frequencies for Multidimensional Portfolios," Papers 1510.05097,, revised Sep 2017.
    3. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478,, revised Sep 2007.
    4. 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.
    5. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    6. Aleš Černý, 2003. "Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets," Review of Finance, European Finance Association, vol. 7(2), pages 191-233.
    7. Kallsen Jan & Rheinländer Thorsten, 2011. "Asymptotic utility-based pricing and hedging for exponential utility," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 17-36, March.

    More about this item


    Option pricing; Incomplete markets; Local utility; Neutral derivative price; Sensitivity process; Local sensitivity;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models


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