报告题目：Optimal Consumption under Relaxed Benchmark Tracking and Consumption Drawdown Constraint
时 间：2026年6月22日（星期一）11：00
地 点：科研楼18号楼1102
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：This report focuses on an optimal consumption problem involving both relaxed benchmark tracking and a consumption drawdown constraint. The paper models the fund manager’s strategic capital injection behavior under the benchmark tracking requirement, ensuring that the total capital process consistently outperforms a benchmark process described by geometric Brownian motion. To solve the resulting stochastic control problem with dynamic state-control constraints, the authors first transform the original regular-singular control problem into an equivalent regular control problem with a reflected state process and a consumption drawdown constraint. They then apply a dual transformation and characterize optimal consumption behavior, reducing the problem to a linear dual PDE with Neumann and free-boundary conditions across different regions. By using the smooth-fit principle and the supercontact condition, the paper derives a closed-form solution and obtains the optimal investment and consumption strategies in feedback form. Finally, a verification theorem is established with the help of an auxiliary reflected dual process and technical estimates, while numerical examples are provided to illustrate the financial implications of the model.
报告人简介：闫凯昕，厦门大学在读博士生。2020年本科毕业于山东大学统计学专业，获理学学士学位；2020年至今于厦门大学数学科学学院攻读统计学博士学位，预计2026年6月毕业。主要研究方向为金融数学和精算科学。2023年7月至2024年10月在香港理工大学应用数学系担任研究助理，2024年11月至2026年4月受国家留学基金委资助赴巴黎综合理工学院应用数学中心联合培养。近年来在 Mathematics of Operations Research、SIAM Journal on Control and Optimization、SIAM Journal on Financial Mathematics、Advances in Applied Probability、Scandinavian Actuarial Journal、中国科学：数学等期刊发表或录用多篇论文。