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A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization

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  • Zhou Yang
  • Junkee Jeon

Abstract

In this paper, we undertake an investigation into the utility maximization problem faced by an economic agent who possesses the option to switch jobs, within a scenario featuring the presence of a mandatory retirement date. The agent needs to consider not only optimal consumption and investment but also the decision regarding optimal job-switching. Therefore, the utility maximization encompasses features of both optimal switching and stochastic control within a finite horizon. To address this challenge, we employ a dual-martingale approach to derive the dual problem defined as a finite-horizon pure optimal switching problem. By applying a theory of the double obstacle problem with non-standard arguments, we examine the analytical properties of the system of parabolic variational inequalities arising from the optimal switching problem, including those of its two free boundaries. Based on these analytical properties, we establish a duality theorem and characterize the optimal job-switching strategy in terms of time-varying wealth boundaries. Furthermore, we derive integral equation representations satisfied by the optimal strategies and provide numerical results based on these representations.

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  • Zhou Yang & Junkee Jeon, 2023. "A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization," Papers 2309.12588, arXiv.org.
    • Handle: RePEc:arx:papers:2309.12588
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    References listed on IDEAS

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    1. Zhou Yang & Hyeng Keun Koo, 2018. "Optimal Consumption and Portfolio Selection with Early Retirement Option," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1378-1404, November.
    2. Jeon, Junkee & Kim, Geonwoo, 2019. "An integral equation approach for optimal investment policies with partial reversibility," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 73-78.
    3. 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.
    4. Jeon, Junkee & Park, Kyunghyun, 2023. "Optimal job switching and retirement decision," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    5. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    6. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    7. Min Dai & Zhou Yang & Qing Zhang & Qiji Jim Zhu, 2016. "Optimal Trend Following Trading Rules," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 626-642, May.
    8. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing European continuous-installment strangle options," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    9. 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.
    10. Randall Martyr, 2016. "Finite-Horizon Optimal Multiple Switching with Signed Switching Costs," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1432-1447, November.
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