9I果冻制作厂

　　题目：A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization

　　报告人： 杨舟

　　时?间：2024年11月3日（周日），上午9：00-10：00

　　报告地点：理学院1-301会议室

　　报告摘要：

　　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.

　　报告人介绍：

　　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：美式衍生产物定价、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 FINANC MATH、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。