Optimal active management fees

We consider the problem of a mutual fund manager that maximizes the present value of expected fees and has to decide the level of fee to impose on the fund. The fee will be paid by a risk averse investor that maximizes expected utility over final wealth. This investor can invest either in an indexed fund or in a managed fund. The manager has superior ability and, as a result of it, the fund offers a higher expected return. However, the investor has incomplete information about the ability of the fund manager. The investor has priors about this ability that are upgraded according to the performance of the fund. At some optimal level, the investor decides to switch from the market portfolio to the mutual fund. Our problem does not have a closed form solution, but we can compute optimal fees, using simulation.