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Pricing Via Utility Maximization and Entropy

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  • Richard Rouge
  • Nicole El Karoui
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    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..

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 10 (2000)
    Issue (Month): 2 ()
    Pages: 259-276

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    Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:259-276

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