  In this paper we solve the hedge fund manager's optimization problem in a
model that allows for investors to enter and leave the fund over time depending
on its performance. The manager's payoff at the end of the year will then
depend not just on the terminal value of the fund level, but also on the lowest
and the highest value reached over that time. We establish equivalence to an
optimal stopping problem for Brownian motion; by approximating this problem
with the corresponding optimal stopping problem for a random walk we are led to
a simple and efficient numerical scheme to find the solution, which we then
illustrate with some examples.
