Stochastic correlation in exponential utility indifference valuation

We consider the problem of exponential utility indifference valuation for a contingent claim H in an incomplete market driven by two Brownian motions. The claim depends on an untradable asset which is stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the dynamic value process V of the exponential utility maximization with the claim H as random endowment. This yields an explicit formula for the indifference value at any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended. In particular, our approach helps to understand the role of the distortion power appearing in the PDE approach to the same problem in a Markovian setting. The key to explaining why all this works is a new result which shows that V has a certain (subtle) monotonicity property with respect to correlation.
(Of course, all concepts from finance will be explained in the talk, whose main focus will be on the mathematical aspects of the problem.)

This is joint work with Christoph Frei (ETH Zürich).