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On optimal reinsurance, dividend and reinvestment strategies

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  • Meng, Hui
  • Siu, Tak Kuen

Abstract

We investigate an optimal reinsurance and dividend problem of an insurance company with the presence of reinvestments, or retained earnings. We consider the general situation that the company needs to pay both fixed and proportional costs. The object of the company is to determine reinsurance, dividend and reinvestment strategies so as to maximize the difference between the expected discounted dividends minus the expected discounted reinvestment until the time of ruin. We focus on the excess-of-loss reinsurance strategy, which is shown to be optimal. The mixed classical-impulse control is then used to discuss the problem. Using inventory control theory, the value function and optimal strategy are derived.

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  • Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    • Handle: RePEc:eee:ecmode:v:28:y:2011:i:1-2:p:211-218
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    Cited by:

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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. Sancho Salcedo-Sanz & Leo Carro-Calvo & Mercè Claramunt & Ana Castañer & Maite Mármol, 2014. "Effectively Tackling Reinsurance Problems by Using Evolutionary and Swarm Intelligence Algorithms," Risks, MDPI, vol. 2(2), pages 1-14, April.
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    6. Liang, Zhibin & Young, Virginia R., 2012. "Dividends and reinsurance under a penalty for ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 437-445.
    7. Cheng, Gongpin & Zhao, Yongxia, 2016. "Optimal risk and dividend strategies with transaction costs and terminal value," Economic Modelling, Elsevier, vol. 54(C), pages 522-536.
    8. Yang, Bo & Wang, Yizhi & Yao, Dingjun & Wang, Yueyang & Xu, Xin, 2024. "The equilibrium strategy of insurance companies’ dividends and reinsurance games," Economics Letters, Elsevier, vol. 245(C).
    9. Meng, Hui & Liao, Pu & Siu, Tak Kuen, 2019. "Continuous-time optimal reinsurance strategy with nontrivial curved structures," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    11. 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.

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