We address the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where price process of risky assets follows a stochastic volatility model and we require that investors observe just the vector of stock prices. Using stochastic filtering techniques and adapting martingale duality methods in this partially observed incomplete model, we characterize the value function and the optimal portfolio policies. We study in detail the Bayesian case, when risk premia of the stochastic volatility model are unobservable random variables with known prior distribution. We also consider the case of unobservable risk premia modelled by linear Gaussian processes.