时 间：2026年10月30日 10:00-11:30
地 点：普陀校区理科大楼 A1414室
报告人：杨舟 华南师范大学 教授
主持人：危佳钦 华东师范大学统计学院
摘 要：
This paper investigates the finite-horizon optimal investment-consumption problem with voluntary retirement and upper and lower bounds on consumption, which can be formulated as a mixed stochastic control problem coupling stopping and constrained regular controls. Different from the conventional duality method for such problems, we adopt a direct approach in this paper: we first derive the Hamilton-Jacobi-Bellman equation for the original mixed control problem, and obtain its dual equation via the Legendre transformation; then, we analyze the analytical properties of the solution and free boundaries to the dual equation based on partial differential equation theory; finally, we prove the corresponding verification theorem using these properties, and theoretically study the key characteristics of the optimal strategies, focusing on the regularity of the three free boundaries (the optimal retirement boundary, the upper consumption boundary and the lower consumption boundary) as well as their monotonicity with respect to the initial time, initial wealth and model parameters.
报告人简介：
杨舟，华南师范大学数学科学学院，教授，博士导师。主要从事金融数学和随机控制方面的研究，主要研究方向为：美式衍生产品定价、最优投资组合、最优停时问题、金融中的自由边界问题。部分研究成果发表于FINANC STOCH、SMATH OPER RES、SIAM J CONTROL OPTIM、SIAM J FINANC MATH、SIAM J MATH ANAL、J DIFFER EQUATIONS等期刊。曾主持六项国家基金和多项省部级基金。