Dynamic exponential utility indifference valuation

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 SE arrow 0 or alpha NE arrow infinity to our general setting. Moreover, we also prove convergence of the corresponding hedging strategies.