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August 2005 Dynamic exponential utility indifference valuation
Michael Mania, Martin Schweizer
Ann. Appl. Probab. 15(3): 2113-2143 (August 2005). DOI: 10.1214/105051605000000395


We study the dynamics of the exponential utility indifference value process C(B; α) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B; α) 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 Ct(B; α). We obtain continuity in B and local Lipschitz-continuity in the risk aversion α, uniformly in t, and we extend earlier results on the asymptotic behavior as α↘0 or α↗∞ to our general setting. Moreover, we also prove convergence of the corresponding hedging strategies.


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Michael Mania. Martin Schweizer. "Dynamic exponential utility indifference valuation." Ann. Appl. Probab. 15 (3) 2113 - 2143, August 2005.


Published: August 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1134.91449
MathSciNet: MR2152255
Digital Object Identifier: 10.1214/105051605000000395

Primary: 60G48 , 60H10 , 91B16 , 91B28

Keywords: BMO-martingales , BSDE , dynamic valuation , exponential utility , incomplete markets , Indifference value , minimal entropy martingale measure , semimartingale backward equation

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.15 • No. 3 • August 2005
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