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Pricing Via Utility Maximization and Entropy

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  • Richard Rouge
  • Nicole El Karoui

Abstract

In a financial market model with constraints on the portfolios, define the price for a claim "C" as the smallest real number "p" such that sup π E["U"("X" "T" -super-"x"+"p",&thin sp;π - "C")]≥ sup π E["U"("X" "T" -super-"x", π)] , where "U" is the negative exponential utility function and "X"-super-"x", π is the wealth associated with portfolio π and initial value "x". We give the relations of this price with minimal entropy or fair price in the flavor of Karatzas and Kou (1996) and superreplication. Using dynamical methods, we characterize the price equation, which is a quadratic Backward SDE, and describe the optimal wealth and portfolio. Further use of Backward SDE techniques allows for easy determination of the pricing function properties. Copyright Blackwell Publishers, Inc..

Suggested Citation

  • Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276.
  • Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:259-276
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    References listed on IDEAS

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    1. Rheinländer, Thorsten & Schweizer, Martin, 1997. "On L2-projections on a space of stochastic integrals," SFB 373 Discussion Papers 1997,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, pages 385-413.
    3. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    4. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198.
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