Dynamic exponential utility indifference valuation

Details Dynamic exponential utility indifference valuation Dynamic exponential utility indifference valuation

2005-08-25

arxiv.org/abs/math/0508489v1

Annals of Applied Probability 2005, Vol. 15, No. 3, 2113-2143

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000395 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000395

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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