Optimal consumption and investment with a costly reversible job-switching option

Gyoocheol Shim () and Junkee Jeon ()
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Gyoocheol Shim: Ajou University
Junkee Jeon: Kyung Hee University

Mathematical Methods of Operations Research, 2025, vol. 101, issue 3, No 4, 459-506

Abstract: Abstract In this paper, we investigate an optimal consumption and investment problem for an economic agent who possesses the option to switch jobs. We assume that two types of jobs are available. One type offers higher income but also entails a greater level of disutility from labor compared to the other type. The option to switch jobs is reversible, enabling the agent to transition between them at any time, albeit incurring a cost. Our utility maximization problem involves aspects of both optimal switching and stochastic control. By employing the martingale-duality approach, we reduce the maximization problem to a pure optimal switching problem. This problem encompasses a system of two variational inequalities, which admits a continuously differentiable and closed-form solution. We fully characterize the optimal job-switching strategy based on two free boundaries. Furthermore, we derive a closed-form solution for the optimal consumption and portfolio strategy through the duality relationship.

Keywords: Consumption and investment; Job-switching with costs; Disutility; Optimal switching problem; A system of two variational inequality (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00899-y

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