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Stochastic control with inhomogeneous regime switching: Application to consumption and investment with unemployment and reemployment

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  • Tao, Cheng
  • Rong, Ximin
  • Zhao, Hui

Abstract

This paper presents a stochastic control problem with an inhomogeneous regime switching and applies it to a consumption and investment model. We prove that the inhomogeneous Markov chain is a semimartingale, providing a basis to extend the HJB equations with regime switching to inhomogeneous cases. Explicit solutions are obtained by solving the corresponding HJB equations. Additionally, we study the impact of different levels of unemployment income and intensities of unemployment and reemployment on consumption and value function. Our findings suggest that improving unemployment security and reemployment intensity can increase overall happiness and improve the total value function.

Suggested Citation

  • Tao, Cheng & Rong, Ximin & Zhao, Hui, 2023. "Stochastic control with inhomogeneous regime switching: Application to consumption and investment with unemployment and reemployment," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    • Handle: RePEc:eee:mateco:v:107:y:2023:i:c:s0304406823000423
    DOI: 10.1016/j.jmateco.2023.102849
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    References listed on IDEAS

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    1. Pirvu, Traian A. & Zhang, Huayue, 2014. "Investment–consumption with regime-switching discount rates," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 142-150.
    2. Brinker, Leonie Violetta & Eisenberg, Julia, 2021. "Dividend optimisation: A behaviouristic approach," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 202-224.
    3. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
    4. 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.
    5. Jang, Bong-Gyu & Park, Seyoung & Rhee, Yuna, 2013. "Optimal retirement with unemployment risks," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3585-3604.
    6. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
    7. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    8. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    9. Chen, An & Hentschel, Felix & Steffensen, Mogens, 2021. "On retirement time decision making," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 107-129.
    10. 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.
    11. Jang, Bong-Gyu & Park, Seyoung & Zhao, Huainan, 2020. "Optimal retirement with borrowing constraints and forced unemployment risk," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 25-39.
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