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

Geonwoo Kim and Junkee Jeon ()
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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 23, 1-18

Abstract: 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.

Keywords: consumption ratcheting; early retirement; effort choice labor supply; singular control; optimal stopping problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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