  We develop a technique based on Malliavin-Bismut calculus ideas, for
asymptotic expansion of dual control problems arising in connection with
exponential indifference valuation of claims, and with minimisation of relative
entropy, in incomplete markets. The problems involve optimisation of a
functional of Brownian paths on Wiener space, with the paths perturbed by a
drift involving the control. In addition there is a penalty term in which the
control features quadratically. The drift perturbation is interpreted as a
measure change using the Girsanov theorem, leading to a form of the integration
by parts formula in which a directional derivative on Wiener space is computed.
This allows for asymptotic analysis of the control problem. Applications to
incomplete It\^o process markets are given, in which indifference prices are
approximated in the low risk aversion limit. We also give an application to
identifying the minimal entropy martingale measure as a perturbation to the
minimal martingale measure in stochastic volatility models.
