讲座题目：A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization
主讲人：杨舟 教授
主持人：危佳钦 教授
开始时间：2024-12-06 10:00
讲座地址：普陀校区理科大楼A1714
主办单位：统计学院
报告人简介：
杨舟，华南师范大学数学科学学院，教授，博士生导师。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MATH OPER RES、SIAM J CONTROL OPTIM、SIAM J MATH ANAL、J DIFFER EQUATIONS等期刊。曾主持五项国家基金和多项省部级基金。
报告内容：
In this paper, we undertake an investigation into the utility maximization problem faced by an economic agent who possesses the option to switch jobs, within a scenario featuring the presence of a mandatory retirement date. The agent needs to consider not only optimal consumption and investment but also the decision regarding optimal job-switching. Therefore, the utility maximization encompasses features of both optimal switching and stochastic control within a finite horizon. To address this challenge, we employ a dual-martingale approach to derive the dual problem defined as a finite-horizon pure optimal switching problem. By applying a theory of the double obstacle problem with non-standard arguments, we examine the analytical properties of the system of parabolic variational inequalities arising from the optimal switching problem, including those of its two free boundaries. Based on these analytical properties, we establish a duality theorem and characterize the optimal job-switching strategy in terms of time-varying wealth boundaries. Furthermore, we derive integral equation representations satisfied by the optimal strategies and provide numerical results based on these representations.
