  The mean-variance hedging (MVH) problem is studied in a partially observable
market where the drift processes can only be inferred through the observation
of asset or index processes. Although most of the literatures treat the MVH
problem by the duality method, here we study a system consisting of three BSDEs
derived by Mania and Tevzadze (2003) and Mania et.al.(2008) and try to provide
more explicit expressions directly implementable by practitioners. Under the
Bayesian and Kalman-Bucy frameworks, we find that a relevant BSDE yields a
semi-closed solution via a simple set of ODEs which allow a quick numerical
evaluation. This renders remaining problems equivalent to solving European
contingent claims under a new forward measure, and it is straightforward to
obtain a forward looking non-sequential Monte Carlo simulation scheme. We also
give a special example where the hedging position is available in a semi-closed
form. For more generic setups, we provide explicit expressions of approximate
hedging portfolio by an asymptotic expansion. These analytic expressions not
only allow the hedgers to update the hedging positions in real time but also
make a direct analysis of the terminal distribution of the hedged portfolio
feasible by standard Monte Carlo simulation.
