  We study the optimal asset allocation problem for a fund manager whose
compensation depends on the performance of her portfolio with respect to a
benchmark. The objective of the manager is to maximise the expected utility of
her final wealth. The manager observes the prices but not the values of the
market price of risk that drives the expected returns. The estimates of the
market price of risk get more precise as more observations are available. We
formulate the problem as an optimization
  under partial information. The particular structure of the incentives makes
the objective function not concave. We solve the problem via the martingale
method and, with a concavification procedure, we obtain the optimal wealth and
the investment strategy. A numerical example shows the effect of learning on
the optimal strategy.
