Abstract

In this paper we present a mathematical framework for the optimal investment problem of a fund manager who gets paid a performance fee and a management fee from his investors. Through the equivalence to an optimal stopping problem, we find a simple characterisation of the solution and an early indicator that performance fees provide precarious incentives. We then incorporate more detailed specifications of the fee structure. The effects of a high-water mark, a hurdle rate or a manager’s personal stake can all be demonstrated elegantly. Finally, we increase the complexity of our model by relaxing the conditions on the underlying assets and allowing for investors to enter and leave the fund over time, according to its performance. Our framework still allows for an illustrative characterisation of the manager’s incentivisation in this case and we turn to numerical methods to demonstrate concrete examples.