Abstract: The problems of non-concave utility maximization appear in many areas, such as in behavior economics, incentive schemes, and goal problems. The standard approach to solving these problems is to use the concavification principle. We provide a framework for solving non-concave utility maximization problems, where the concavification principle may not hold and the utility functions can be discontinuous. In particular, we find that adding portfolio constraints, which makes the concavification principle invalid, can significantly affect economic insights in the existing literature. Theoretically, we show that a monotone, stable, and consistent finite difference numerical scheme still converges to the value function under the framework. This work is jointly with Steven Kou, Shuaijie Qian, and Xiangwei Wan.

Bio: 戴民教授现任新加坡国立大学教授、数量金融中心主任、数量金融硕士项目主管。专长金融衍生产品定价与对冲、动态投资策略、缺乏流动性的投资组合设计。在数理金融、经济、金融、管理领域期刊发表了一些深入的工作。目前担任Journal of Economic Dynamics & Control、SIAM Journal on Financial Mathematics、Mathematics and Financial Economics等期刊编委及Digital Finance期刊联合主编。