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Optimal financing and dividend control of the insurance company with proportional reinsurance policy

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  • He, Lin
  • Liang, Zongxia

Abstract

We consider the optimal control problem of the insurance company with proportional reinsurance policy. The management of the company controls the reinsurance rate, dividends payout as well as the equity issuance processes to maximize the expected present value of the dividends minus the equity issuance until the time of bankruptcy. This is the first time that the financing process in an insurance model has been considered, which is more realistic. To find the solution of the mixed singular-regular control problem, we firstly construct two categories of suboptimal models, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance. Then we identify the value functions and the optimal strategies corresponding to the suboptimal models depending on the relationships between the coefficients.

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  • He, Lin & Liang, Zongxia, 2008. "Optimal financing and dividend control of the insurance company with proportional reinsurance policy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 976-983, June.
  • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:976-983
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    Cited by:

    1. Zhu, Jinxia & Yang, Hailiang, 2016. "Optimal capital injection and dividend distribution for growth restricted diffusion models with bankruptcy," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 259-271.
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    3. Guan, Huiqi & Liang, Zongxia, 2014. "Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 109-122.
    4. Sheng Delei, 2016. "Explicit Solution of the Optimal Reinsurance-Investment Problem with Promotion Budget," Journal of Systems Science and Information, De Gruyter, vol. 4(2), pages 131-148, April.
    5. Zongxia Liang & Bin Sun, 2010. "Optimal control of a big financial company with debt liability under bankrupt probability constraints," Papers 1007.5376, arXiv.org, revised Aug 2010.
    6. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    7. Liang, Zongxia & Huang, Jianping, 2011. "Optimal dividend and investing control of an insurance company with higher solvency constraints," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 501-511.
    8. Jinxia Zhu & Hailiang Yang, 2015. "Optimal financing and dividend distribution in a general diffusion model with regime switching," Papers 1506.08360, arXiv.org.
    9. Zongxia Liang & Lin He & Jiaoling Wu, 2010. "Optimal Dividend and reinsurance strategy of a Property Insurance Company under Catastrophe Risk," Papers 1009.1269, arXiv.org.
    10. Zhu, Jinxia & Chen, Feng, 2015. "Dividend optimization under reserve constraints for the Cramér–Lundberg model compounded by force of interest," Economic Modelling, Elsevier, vol. 46(C), pages 142-156.
    11. He, Lin & Liang, Zongxia, 2013. "Optimal dynamic asset allocation strategy for ELA scheme of DC pension plan during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 404-410.
    12. Kristoffer Lindensjo & Filip Lindskog, 2019. "Optimal dividends and capital injection under dividend restrictions," Papers 1902.06294, arXiv.org.
    13. Chonghu Guan & Zuo Quan Xu & Rui Zhou, 2020. "Dynamic optimal reinsurance and dividend-payout in finite time horizon," Papers 2008.00391, arXiv.org, revised Jun 2022.
    14. Ernst, Philip A. & Imerman, Michael B. & Shepp, Larry & Zhou, Quan, 2022. "Fiscal stimulus as an optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1091-1108.
    15. Guan, Guohui & Liang, Zongxia & Feng, Jian, 2018. "Time-consistent proportional reinsurance and investment strategies under ambiguous environment," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 122-133.
    16. Hongshuai Dai & Zaiming Liu & Nana Luan, 2010. "Optimal dividend strategies in a dual model with capital injections," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 129-143, August.
    17. Kristoffer Lindensjö & Filip Lindskog, 2020. "Optimal dividends and capital injection under dividend restrictions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 461-487, December.
    18. Zhou, Ming & Yuen, Kam C., 2012. "Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle," Economic Modelling, Elsevier, vol. 29(2), pages 198-207.
    19. He, Lin & Liang, Zongxia, 2013. "Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 643-649.
    20. Chen, Mi & Peng, Xiaofan & Guo, Junyi, 2013. "Optimal dividend problem with a nonlinear regular-singular stochastic control," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 448-456.
    21. Xiaoxiao Zheng & Xin Zhang, 2014. "Optimal investment-reinsurance policy under a long-term perspective," Papers 1406.7604, arXiv.org.
    22. Liu, Wei & Hu, Yijun, 2014. "Optimal financing and dividend control of the insurance company with excess-of-loss reinsurance policy," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 121-130.
    23. He, Lin & Hou, Ping & Liang, Zongxia, 2008. "Optimal control of the insurance company with proportional reinsurance policy under solvency constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 474-479, December.

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