2021/07/25 by Junkee Jeon, Jeon, Junkee, Hyeng Keun Koo +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G40 #91A15 #91G10 #93E20 #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #msc:60G40 #msc:91A15 #msc:91G10 #msc:93E20
paper · pdf · doi:10.48550/arxiv.2107.11735
34pages
openalex publication_date 2021/07/25 · arxiv created 2021/07/27 · arxiv updated 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We transform the problem into a dual two-person zero-sum game, which involves a controller, who is a minimizer and chooses a non-increasing process, and a stopper, who is a maximizer and chooses a stopping time. We derive the Hamilton-Jacobi- Bellman quasi-variational inequality(HJBQV) of a max-min type arising from the game. We provide a solution to the HJBQV and verification that it is the value of the game. We establish a duality result which allows to derive the optimal strategies and value function of the primal problem from those of the dual problem.