A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization
報告人簡介
楊舟，華南師范大學數學科學學院，教授，博士導師。主要從事金融數學和隨機控制方面的研究，主要研究方向為：美式衍生產品定價、最優投資組合、最優停時問題、金融中的自由邊界問題。部分研究成果發表于MATH OPER RES、SIAM J CONTROL OPTIM、SIAM J MATH ANAL、J DIFFER EQUATIONS等期刊。曾主持五項國家基金和多項省部級基金。
內容簡介
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.
