Optimal Consumption and Investment with Income Adjustment and Borrowing Constraints

Geonwoo Kim and Junkee Jeon ()
Additional contact information
Geonwoo Kim: School of Natural Sciences, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
Junkee Jeon: Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of Korea

Mathematics, 2024, vol. 12, issue 22, 1-14

Abstract: In this paper, we address the utility maximization problem of an infinitely lived agent who has the option to increase their income. The agent can increase their income at any time, but doing so incurs a wealth cost proportional to the amount of the increase. To prevent the agent from infinitely increasing their income and borrowing against future income, we additionally consider a non-negative wealth constraint that prohibits borrowing based on future income. This utility maximization problem is a mixture of stochastic control, where the agent chooses consumption and investment, and singular control, where the agent chooses a non-decreasing income process. To solve this non-trivial and challenging problem, we derive the Hamilton–Jacobi–Bellman (HJB) equation with a gradient constraint using the dynamic programming principle (DPP). Then, using the guess-and-verify method and a linearization technique, we obtain a closed-form solution to the HJB equation and, based on this, find the optimal strategy.

Keywords: income adjustment; consumption and investment; HJB equation; singular control; free boundary problem; linearization; borrowing constraint (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/22/3536/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/22/3536/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:22:p:3536-:d:1519427

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().