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Optimal portfolio and retirement decisions with costly job switching options

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  • An, Jongbong
  • Jeon, Junkee
  • Kim, Takwon

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.

Suggested Citation

  • An, Jongbong & Jeon, Junkee & Kim, Takwon, 2025. "Optimal portfolio and retirement decisions with costly job switching options," Applied Mathematics and Computation, Elsevier, vol. 491(C).
    • Handle: RePEc:eee:apmaco:v:491:y:2025:i:c:s0096300324006763
    DOI: 10.1016/j.amc.2024.129215
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    References listed on IDEAS

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    1. Jeon, Junkee & Park, Kyunghyun, 2023. "Optimal job switching and retirement decision," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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    4. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    6. Randall Martyr, 2016. "Finite-Horizon Optimal Multiple Switching with Signed Switching Costs," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1432-1447, November.
    7. Mihail Zervos & Carlos Oliveira & Kate Duckworth, 2018. "An investment model with switching costs and the option to abandon," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 417-443, December.
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