2023/09/22 by Zhou Yang, Yang, Zhou, Junkee Jeon +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #35Q93 #35R35 #91G10 #93E20 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2309.12588
openalex publication_date 2023/09/22 · openalex created_date 2023/09/26 · openalex updated_date 2026/07/28
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.