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

　　報(bào)告人： 楊舟

　　時(shí)?間：2024年11月3日（周日），上午9：00-10：00

　　報(bào)告地點(diǎn)：理學(xué)院1-301會(huì)議室

　　報(bào)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.

　　報(bào)告人簡(jiǎn)介：

　　楊舟,，華南師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院,，教授,，博士導(dǎo)師。主要從事金融數(shù)學(xué)和隨機(jī)控制方面的研究,，主要研究方向?yàn)椋好朗窖苌a(chǎn)品定價(jià),、最優(yōu)投資組合、最優(yōu)停時(shí)問題,、金融中的自由邊界問題,。部分研究成果發(fā)表于MATH OPER RES、SIAM J CONTROL OPTIM,、SIAM J FINANC MATH,、SIAM J MATH ANAL、J DIFFER EQUATIONS等期刊,。曾主持五項(xiàng)國(guó)家基金和多項(xiàng)省部級(jí)基金,。