Multi-period mean–variance portfolio optimization with management fees

Due to limited capital and limited information from stock market, some individual investors prefer to construct a portfolio of funds instead of stocks. But, there will be management fees paid to the fund managers during the investment, which are in general proportional to the net asset value of the funds. Motivated by this phenomena, this paper considers multi-period mean–variance portfolio optimization problem with proportional management fees. Using stochastic dynamic programming, we derive the semi-analytical optimal portfolio policy. Our result helps clarify the benefit and cost of adopting such dynamic portfolio policy with management fees.