Optimal portfolio and retirement decisions with costly job switching options

Jongbong An, Junkee Jeon and Takwon Kim

Applied Mathematics and Computation, 2025, vol. 491, issue C

Abstract: In this paper, we consider the utility maximization problem of an agent regarding optimal consumption-investment, job-switching strategy, and the optimal early retirement date. The agent can switch between two jobs or job categories at any time before retirement, but incurs a cost when switching to a position offering higher labor income. The agent's utility maximization involves a combination of stochastic control for consumption and investment, switching control for job-switching, and optimal stopping for early retirement decisions, making it a non-trivial and highly challenging problem. By utilizing the dynamic programming principle, we can derive the nonlinear Hamilton-Jacobi-Bellman (HJB) equation in the form of a system of variational inequalities with obstacle constraints, which arises from the agent's optimization problem. We employ guess and verify methods based on economic intuition to derive the closed-form solution of this HJB equation and demonstrate, through a verification theorem, that this solution aligns with the solution to the agent's utility maximization problem.

Keywords: Utility maximization; Job switching with costs; Early retirement; Consumption and investment; Optimal switching; Optimal stopping; Stochastic control; HJB equation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:491:y:2025:i:c:s0096300324006763

DOI: 10.1016/j.amc.2024.129215

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