Dynamic exponential utility indifference valuation

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