We examine optimal hedging of a claim on a non-traded asset, using a correlated traded asset, when one does not know with certainty the values of the asset price drifts. In this partial information setting, the uncertain parameters are considered as random variables. We filter the drifts from price observations, updating a chosen prior distribution. The result is an effective full information model with random drift parameters. Using a dual approach, we derive representations for the indifference price and optimal hedging strategy, with exponential utility. Using the marginal utility-based price as an approximation to the indifference price, analytic formulae for the optimal hedge are possible, and this allows a simulation study of the optimal hedging program to be carried out. The results indicate improved hedging performance relative to a Black-Scholes strategy which takes the correlation as perfect, and also relative to a utility-based hedging program which does not incorporate learning
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