Mean-Variance Hedging for Partially Observed Drift Processes

We consider the mean-variance hedging when an investor observes just the stock prices. We explain how the theory developed in Gouriéroux, Laurent and Pham (1998) and Rheinländer and Schweizer (1997) can be extended to this framework. We then focus to a diffusion model when drift of stock prices are not observed directly but only through a measurement process. By using filtering techniques, we obtain explicit formulae for optimal mean-variance hedging strategies and for the associated minimal risk. Closed-form expressions are provided in the case of a Bayesian investor and when the stock drift is modelled as a linear Gaussian process.