Previous Issue
Volume 14, July-2
 
 
mathematics-logo

Journal Browser

Journal Browser

Mathematics, Volume 14, Issue 15 (August-1 2026) – 1 article

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Select all
Export citation of selected articles as:
28 pages, 909 KB  
Article
Optimal Consumption and Investment with Early Retirement Under a Target Wealth Constraint
by Geonwoo Kim and Junkee Jeon
Mathematics 2026, 14(15), 2668; https://doi.org/10.3390/math14152668 (registering DOI) - 23 Jul 2026
Abstract
We study an infinite-horizon consumption, portfolio, and early-retirement problem for a wage earner who receives labor income while working but bears a constant utility cost of labor. Retirement is irreversible and removes both labor income and work disutility. In addition, retirement is feasible [...] Read more.
We study an infinite-horizon consumption, portfolio, and early-retirement problem for a wage earner who receives labor income while working but bears a constant utility cost of labor. Retirement is irreversible and removes both labor income and work disutility. In addition, retirement is feasible only after the agent has accumulated a prescribed level of financial wealth. We solve the problem under constant relative risk aversion using a dual martingale method. The post-retirement problem reduces to the standard Merton problem, while the pre-retirement problem becomes an optimal stopping problem with a target-induced obstacle. We derive an explicit dual value function, characterize the free boundary, recover the primal value, and obtain closed-form consumption, portfolio, and retirement policies. The solution exhibits a sharp slack–binding dichotomy: small targets do not affect the classical disutility retirement policy, whereas large targets become the effective retirement threshold and reshape both consumption and risky investment before retirement. Full article
Show Figures

Figure 1

Previous Issue
Back to TopTop