Analysis of the optimal time to withdraw investments from hedge funds with alternative fee structures

Abstract

We study the optimal stopping problem arising from an investor determining the optimal time to withdraw from a hedge fund investment with a shared loss fee structure and a positive fee for assets under management. The optimal solution is characterized as the first exit time of the fund value from a bounded region with upper and lower stopping boundaries. In the infinite horizon case, we present the complete solution to the optimal stopping problem, while in the finite horizon case we derive a pair of coupled integral equations for the stopping bounds, and present an asymptotic analysis of the stopping boundaries for small time.