Dynamic Asset Allocation and Retirement Decision with Consumption Ratcheting and Effort Choice

This study examines the problem of choosing optimal consumption, investment, early retirement, and effort levels for an economic agent who is unwilling to reduce their consumption over time. The agent’s income depends on a fixed wage rate, and varies proportionally with their level of effort, which...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-12, Vol.12 (23), p.3821
Main Authors: Kim, Geonwoo, Jeon, Junkee
Format: Article
Language:English
Subjects:
Closed form solutions
Consumption
consumption ratcheting
Decision making
Early retirement
effort choice labor supply
Flexibility
Investment policy
Investments
Labor supply
Martingales
optimal stopping problem
Optimization
Retirement
singular control
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Summary:This study examines the problem of choosing optimal consumption, investment, early retirement, and effort levels for an economic agent who is unwilling to reduce their consumption over time. The agent’s income depends on a fixed wage rate, and varies proportionally with their level of effort, which incurs disutility due to labor. By applying the dual-martingale method, we reformulate the problem into its dual form, dividing it into two distinct sub-problems: one focuses on selecting a consumption path that does not decrease, while the other determines the optimal timing for early retirement. Using this method, we find optimal strategies in the form of explicit closed-form solutions.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12233821