Optimal Investment And Risk Management For Open-ended Funds

As a type of professionally managed collective investment scheme, mutual funds emerged in 1860s, and soon gained its popularity in America. Benefiting from the scale effect brought by the property of collective investment, mutual funds greatly reduce the transaction cost and make it more easier for individual investors to participate in the capital market. Thus, it has gradually become the mainstream choice for institutional and individual investors.This paper focuses on the open-ended funds and aims to analysis the optimal investment and risk management for large redemption in the perspective of a fund manager. A big difference between open-ended funds and close-ended funds is that investors of open-ended funds can redeem their shares at all times. Close-ended funds always have a lockup period,during which all the shares can only be held and not redeemed. So such a flexible liquidity facility challenges the fund manager of open-ended funds to be capable of risk management, especially for the large redemption.Inspired by the methods used in insurance research, we introduce the com-pound Poisson process to describe the cash flow caused by subscription and re-demption, and also the trigger mechanism of large redemption. Based on the assumption that the prices of underlying risk assets follow the Heston's SV mod-el, we try to maximize the expected exponential utility of the fund manager. And then we obtain the explicit optimal investment and risk management strategies for the fund manager via stochastic optimal control approach. In a simulated scenari-o, the influences of economic variables on our optimal strategies are demonstrated and some economic explanations are given accordingly.Finally, we briefly analyse the guiding significance of our model for a fund manager in practical operations, and make some suggestions for the applicability and extensibility of our model.