Optimal investment strategy under time-inconsistent preferences and high-water mark contract

This paper considers the optimal investment problem for a fund manager who has time-inconsistent preferences and is compensated with a HWM contract. The time preferences of fund manager is described by the stochastic hyperbolic discounting function. The closed-form solution under certain conditions is provided by applying the dynamic programming approach. Interestingly, we find that the sophisticated fund manager is present-biased. The more the fund manager has present-biased preference, there is the greater inclination to increase the proportion in risky asset.