Optimal investment problem for an open-end fund with dynamic flows

ABSTRACT

This paper investigates an optimal investment problem for an open-end fund with dynamic flows. The accumulated fund inflow and outflow processes are modeled by two independent compound Poisson processes, respectively. The fund manager allocates the fund capital between a risk-free asset and a risky asset. The correlation between the fund inflow process and the risky asset's price process is under consideration. Inspired by Berk and Van Binsbergen [(2015). Measuring skill in the mutual fund industry. Journal of Financial Economics, 118(1), 1–20], we first introduce the accumulated value added process to measure the fund performance. The manager aims to maximize the expected utility of the fund's accumulated value added. We derive the optimal investment strategy explicitly via dynamic programming approach. Furthermore, a verification theorem is provided and some properties of the optimal strategy are analyzed. Finally, sensitivity analysis is given to illustrate the effects of model parameters on the optimal strategy.

KEYWORDS:

• Open-end fund
• optimal investment
• dynamic flows
• value added
• Hamilton-Jacobi-Bellman (HJB) equation

Acknowledgments

We would like to thank the referees for their careful reading of the paper and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (Grant Nos. 11771329, 11871052, 11901427).