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Dynamic exponential utility indifference valuation

  • Michael Mania
  • Martin Schweizer
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    We study the dynamics of the exponential utility indifference value process C(B;\alpha) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B;\alpha) is (the first component of) the unique solution of a backward stochastic differential equation with a quadratic generator and obtain BMO estimates for the components of this solution. This allows us to prove several new results about C_t(B;\alpha). We obtain continuity in B and local Lipschitz-continuity in the risk aversion \alpha, uniformly in t, and we extend earlier results on the asymptotic behavior as \alpha\searrow0 or \alpha\nearrow\infty to our general setting. Moreover, we also prove convergence of the corresponding hedging strategies.

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    File URL: http://arxiv.org/pdf/math/0508489
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    Paper provided by arXiv.org in its series Papers with number math/0508489.

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    Date of creation: Aug 2005
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    Publication status: Published in Annals of Applied Probability 2005, Vol. 15, No. 3, 2113-2143
    Handle: RePEc:arx:papers:math/0508489
    Contact details of provider: Web page: http://arxiv.org/

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    1. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, 04.
    2. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    3. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52.
    4. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
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