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In the framework of an incomplete financial market where the stock pricedynamics are modeled by a continuous semimartingale (not necessarily Markovian)an explicit second-order expansion formula for the power investor's valuefunction - seen as a function of the underlying market price of risk process -is provided. This allows us to provide first-order approximations of theoptimal primal and dual controls. Two specific calibrated numerical examplesillustrating the accuracy of the method are also given.

An expansion in the model space in the context of utility maximization