The Annals of Applied Probability

Dynamic exponential utility indifference valuation

Michael Mania and Martin Schweizer

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 3 (2005), 2113-2143.

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1121433779

Digital Object Identifier
doi:10.1214/105051605000000395

Mathematical Reviews number (MathSciNet)
MR2152255

Zentralblatt MATH identifier
1134.91449

Subjects
Primary: 91B28 60H10: Stochastic ordinary differential equations [See also 34F05] 91B16: Utility theory 60G48: Generalizations of martingales

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

Citation

Mania, Michael; Schweizer, Martin. Dynamic exponential utility indifference valuation. Ann. Appl. Probab. 15 (2005), no. 3, 2113--2143. doi:10.1214/105051605000000395. https://projecteuclid.org/euclid.aoap/1121433779


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