Optimal investment based on relative performance and time-varying reference point under VaR and position constraints

We consider the utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a function of the terminal relative performance wealth. The investment manager bases decisions on the terminal payoff comparison to a time-varying reference point. We find the optimal investment strategy by maximizing an S-shaped utility under a VaR and position constraints via a concavification technique and the martingale method. Numerical results are carried out to show the impacts of the incentive scheme and the time-varying reference point on the optimal terminal relative performance.