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Classical and Impulse Control for the Optimization of Dividend and Proportional Reinsurance Policies with Regime Switching

Author

Listed:
  • Jiaqin Wei

    (East China Normal University)

  • Hailiang Yang

    (The University of Hong Kong)

  • Rongming Wang

    (East China Normal University
    Shandong University)

Abstract

We consider the optimal proportional reinsurance and dividend strategy. The surplus process is modeled by the classical compound Poisson risk model with regime switching. Considering a class of utility functions, the object of the insurer is to select the reinsurance and dividend strategy that maximizes the expected total discounted utility of the shareholders until ruin. By adapting the techniques and methods of stochastic control, we study the quasi-variational inequality for this classical and impulse control problem and establish a verification theorem. We show that the optimal value function is characterized as the unique viscosity solution of the corresponding quasi-variational inequality.

Suggested Citation

  • Jiaqin Wei & Hailiang Yang & Rongming Wang, 2010. "Classical and Impulse Control for the Optimization of Dividend and Proportional Reinsurance Policies with Regime Switching," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 358-377, November.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9726-x
    DOI: 10.1007/s10957-010-9726-x
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    References listed on IDEAS

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    8. Albrecher, Hansjörg & Thonhauser, Stefan, 2008. "Optimal dividend strategies for a risk process under force of interest," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 134-149, August.
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    Citations

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    Cited by:

    1. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Center for Mathematical Economics Working Papers 657, Center for Mathematical Economics, Bielefeld University.
    2. Jin, Zhuo & Yang, Hailiang & Yin, G., 2015. "Optimal debt ratio and dividend payment strategies with reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 351-363.
    3. Giorgio Ferrari & Patrick Schuhmann & Shihao Zhu, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Papers 2111.03724, arXiv.org, revised Jun 2022.
    4. Jos'e-Luis P'erez & Kazutoshi Yamazaki & Xiang Yu, 2017. "On the Bail-Out Optimal Dividend Problem," Papers 1709.06348, arXiv.org, revised Jun 2018.
    5. Zhu, Jinxia & Chen, Feng, 2013. "Dividend optimization for regime-switching general diffusions," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 439-456.
    6. Jiang, Zhengjun, 2019. "Optimal dividend policy when risk reserves follow a jump–diffusion process with a completely monotone jump density under Markov-regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 1-7.
    7. Xiaoxiao Zheng & Xin Zhang, 2014. "Optimal Hybrid Dividend Strategy Under The Markovian Regime-Switching Economy," Papers 1406.7606, arXiv.org.
    8. Tim J. Boonen & Engel John C. Dela Vega, 2024. "Optimal Ratcheting of Dividends with Irreversible Reinsurance," Papers 2408.16989, arXiv.org.
    9. José-Luis Pérez & Kazutoshi Yamazaki & Xiang Yu, 2018. "On the Bail-Out Optimal Dividend Problem," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 553-568, November.
    10. Zhuo Jin, 2015. "Optimal Debt Ratio and Consumption Strategies in Financial Crisis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1029-1050, September.
    11. Zhuo Jin & George Yin & Chao Zhu, 2011. "Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation," Papers 1111.2584, arXiv.org.
    12. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2022. "Optimal dividends under Markov-modulated bankruptcy level," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 146-172.
    13. Linlin Tian & Lihua Bai & Junyi Guo, 2020. "Optimal Singular Dividend Problem Under the Sparre Andersen Model," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 603-626, February.

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