Inter‐temporal mutual‐fund management
研究了基金经理在持续收取管理费（行业惯例）下的跨期最优投资问题，通过动态规划原理求解非线性HJB方程，发现不同风险偏好的经理可销售相同投资组合，且高额终期管理费可被极低跨期费用替代，降低客户成本而不影响经理满意度。
Abstract Traditionally, mutual funds are mostly managed via an ad hoc approach, namely a terminal‐only optimization. Due to the intricate mathematical complexity of a continuum of constraints imposed, effects of the inter‐temporal reward for the managers are essentially neglected in the previous literature. For instance, the inter‐temporal optimal investment problem from the fund manager's viewpoint, who earns proportional management fees continuously (a golden rule in practice), has been outstanding for long. This article completely resolves this challenging question especially under generic running and terminal utilities, via the Dynamic Programming Principle which leads to a nonconventional, highly nonlinear HJB equation. We develop an original mathematical analysis to establish the unique existence of the classical solution of the primal problem. Further numerical calibrations and simulations for both the portfolio weight and the value functions illustrate the robustness of the optimal portfolio towards the manager's risk attitude, which allows different managers with various risk characteristics to sell essentially the same investment vehicle. Simulation studies also indicate that the policy of charging a substantial terminal‐only management fee can be replaced by another one with only a negligible amount over the interim period, which substantially reduces the total management fee paid by the clients without lowering the manager's satisfaction at all; this last observation echoes the magic of the alchemy of finance.