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Optimal dividend and scale of business strategies with reinsurance and premium pricing for insurance company

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  • Yao, Dingjun
  • Yang, Bo
  • Xu, Xin
  • Li, Youwei
  • Wang, Yizhi

Abstract

This paper investigates the optimal dividend and business scale strategies aimed at maximizing the value of an insurance company. While prior studies typically assume that insurers can only adjust their business scale through reinsurance, this study extends the framework by allowing the insurer to control the premium rate. Under more realistic market assumptions, we examine the joint optimization problem for two common types of reinsurance — proportional and excess-of-loss — across both arbitrage and non-arbitrage scenarios. We derive the optimal strategies for dividends and premium pricing, along with their corresponding value functions. The results show that the insurer should decrease the premium rate and reduce reinsurance coverage as the surplus increases. The optimal dividend policy follows a barrier strategy. Economic interpretations and numerical examples are provided to illustrate the findings.

Suggested Citation

  • Yao, Dingjun & Yang, Bo & Xu, Xin & Li, Youwei & Wang, Yizhi, 2026. "Optimal dividend and scale of business strategies with reinsurance and premium pricing for insurance company," European Journal of Operational Research, Elsevier, vol. 328(2), pages 694-703.
    • Handle: RePEc:eee:ejores:v:328:y:2026:i:2:p:694-703
    DOI: 10.1016/j.ejor.2025.07.039
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    References listed on IDEAS

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    1. Bing Liu & Ming Zhou & Peng Li, 2020. "Optimal investment and premium control for insurers with ambiguity," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(9), pages 2110-2130, May.
    2. Steffensen, Mogens & Thøgersen, Julie, 2019. "Personal Non-Life Insurance Decisions And The Welfare Loss From Flat Deductibles," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 85-116, January.
    3. 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.
    4. Smith, Clifford Jr. & Watts, Ross L., 1992. "The investment opportunity set and corporate financing, dividend, and compensation policies," Journal of Financial Economics, Elsevier, vol. 32(3), pages 263-292, December.
    5. Avanzi, Benjamin & Lau, Hayden & Wong, Bernard, 2021. "On the optimality of joint periodic and extraordinary dividend strategies," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1189-1210.
    6. Christensen, Bent Jesper & Parra-Alvarez, Juan Carlos & Serrano, Rafael, 2021. "Optimal control of investment, premium and deductible for a non-life insurance company," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 384-405.
    7. Yang, Chen & Sendova, Kristina P. & Li, Zhong, 2020. "Parisian ruin with a threshold dividend strategy under the dual Lévy risk model," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 135-150.
    8. Zhao, Yongxia & Chen, Ping & Yang, Hailiang, 2017. "Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 135-146.
    9. Zhu, Jinxia & Siu, Tak Kuen & Yang, Hailiang, 2020. "Singular dividend optimization for a linear diffusion model with time-inconsistent preferences," European Journal of Operational Research, Elsevier, vol. 285(1), pages 66-80.
    10. Lihua Bai & Junyi Guo & Huayue Zhang, 2010. "Optimal excess-of-loss reinsurance and dividend payments with both transaction costs and taxes," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1163-1172.
    11. Pablo Azcue & Nora Muler, 2005. "Optimal Reinsurance And Dividend Distribution Policies In The Cramér‐Lundberg Model," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 261-308, April.
    12. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    13. Amini, Hamed & Deguest, Romain & Iyidogan, Engin & Minca, Andreea, 2024. "Blockchain adoption and optimal reinsurance design," European Journal of Operational Research, Elsevier, vol. 318(1), pages 341-353.
    14. Aboagye, Ernest & Asimit, Vali & Fung, Tsz Chai & Peng, Liang & Wang, Qiuqi, 2025. "A revisit of the optimal excess-of-loss contract," European Journal of Operational Research, Elsevier, vol. 322(1), pages 341-354.
    15. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2011. "Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs," European Journal of Operational Research, Elsevier, vol. 211(3), pages 568-576, June.
    16. Qianqian Zhou & Junyi Guo, 2020. "Optimal Control of Investment for an Insurer in Two Currency Markets," Papers 2006.02857, arXiv.org.
    17. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2023. "Reinsurance games with two reinsurers: Tree versus chain," European Journal of Operational Research, Elsevier, vol. 310(2), pages 928-941.
    18. Bjarne Hø Jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182, April.
    19. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    20. 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.
    21. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2016. "Optimal Dividend And Reinsurance Strategies With Financing And Liquidation Value," ASTIN Bulletin, Cambridge University Press, vol. 46(2), pages 365-399, May.
    22. Søren Asmussen & Bent Jesper Christensen & Julie Thøgersen, 2019. "Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation," Risks, MDPI, vol. 7(2), pages 1-23, May.
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