# Making mean-variance hedging implementable in a partially observable market

*Masaaki Fujii* and
*Akihiko Takahashi*

*Quantitative Finance*, 2014, vol. 14, issue 10, 1709-1724

**Abstract:**
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 literature treats the MVH problem by the duality method, here we study an equivalent system consisting of three BSDEs and try to provide more explicit expressions directly implementable by practitioners. Under the Bayesian and Kalman-Bucy frameworks, we find that a relevant BSDE can yield a semi-closed solution via a simple set of ODEs which allow quick numerical evaluation. This renders the 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 set-ups, we provide explicit expressions of an 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.

**Date:** 2014

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