Optimal investment with high-watermark performance fee (Q2903504)

The authors propose a general model of profits from dynamic investment in a hedge fund in the form of a stochastic control problem. A special version of the model in the form of two stochastic state equations is obtained based on the assumption that the money market pays zero interest and hinges on the observation that tracking the wealth and accumulated consumption allows to recover the high-watermark. This model is used to solve the resulting stochastic control problem via dynamic programming techniques. It leads to the associated Hamilton-Jacobi-Bellmann equation which has a viscosity solution by Perron's method. The authors prove the existence and representation of the optimal control in feedback form and they analyze the impact of the high-watermark fee. The analysis is appended by some numerical case studies.