Variance-Optimal Martingale Measures for Diffusion Processes with Stochastic Coefficients

In this paper we present the solution of the optimal variance optimal martingale measure for stochastic volatility models, when the noises are correlated. It is proved that the value function of the dual problem is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. The method to develop our results is based on a Bernstein's type of argument. The dual problem of the quadratic hedging problem is studied analyzing the expression obtained after a change of measure, which corresponds to some class of risk-sensitive control problems.