Portfolio selection of a closed‐end mutual fund

A well‐known regulation on the management of a closed‐end mutual fund is that the managers’ account cannot invest in risky assets. This paper studies the impact of this regulation under a given management fee structure such that the cumulative management fee rate is described by a fixed RCLL deterministic increasing function. We conclude that the manager’s welfare is approximately the same whether the regulation exists or not. In the expected utility maximization framework, we explicitly find the optimal investment‐consumption plan when it exists, and get a sequence of asymptotic near‐optimal investment‐consumption plans when an optimal one does not exist.