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Optimal Risk Control for The Excess of Loss Reinsurance Policies

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  • Meng, Hui
  • Zhang, Xin

Abstract

The primary objective of the paper is to explore using reinsurance as a risk management tool for an insurance company. We consider an insurance company whose surplus can be modeled by a Brownian motion with drift and that the surplus can be invested in a risky or riskless asset. Under the above Black-Scholes type framework and using the objective of minimizing the ruin probability of the insurer, we formally establish that the excess-of-loss reinsurance treaty is optimal among the class of plausible reinsurance treaties. We also obtain the optimal level of retention as well as provide an explicit expression of the minimal probability of ruin.

Suggested Citation

  • Meng, Hui & Zhang, Xin, 2010. "Optimal Risk Control for The Excess of Loss Reinsurance Policies," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 179-197, May.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:01:p:179-197_00
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    Citations

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    Cited by:

    1. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
    2. Meng, Hui & Zhou, Ming & Siu, Tak Kuen, 2016. "Optimal reinsurance policies with two reinsurers in continuous time," Economic Modelling, Elsevier, vol. 59(C), pages 182-195.
    3. Zhang, Nan & Jin, Zhuo & Li, Shuanming & Chen, Ping, 2016. "Optimal reinsurance under dynamic VaR constraint," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 232-243.
    4. Matteo Brachetta & Claudia Ceci, 2019. "Optimal excess-of-loss reinsurance for stochastic factor risk models," Papers 1904.05422, arXiv.org.
    5. Linlin Tian & Lihua Bai, 2020. "Minimizing the Ruin Probability under the Sparre Andersen Model," Papers 2004.08124, arXiv.org.
    6. Li, Peng & Zhou, Ming & Yao, Dingjun, 2022. "Optimal time for the excess of loss reinsurance with fixed costs," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 466-475.
    7. Qicai Li & Mengdi Gu & Zhibing Liang, 2014. "Optimal excess-of-loss reinsurance and investment polices under the CEV model," Annals of Operations Research, Springer, vol. 223(1), pages 273-290, December.
    8. Danping Li & Dongchen Li & Virginia R. Young, 2017. "Optimality of Excess-Loss Reinsurance under a Mean-Variance Criterion," Papers 1703.01984, arXiv.org, revised Mar 2017.
    9. Matteo Brachetta & Claudia Ceci, 2019. "Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models," Risks, MDPI, vol. 7(2), pages 1-23, May.
    10. 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.
    11. Xue, Xiaole & Wei, Pengyu & Weng, Chengguo, 2019. "Derivatives trading for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 40-53.
    12. 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.
    13. Liang, Xiaoqing & Young, Virginia R., 2018. "Minimizing the probability of ruin: Optimal per-loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 181-190.
    14. Li, Danping & Li, Dongchen & Young, Virginia R., 2017. "Optimality of excess-loss reinsurance under a mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 82-89.
    15. Bohan Li & Junyi Guo, 2021. "Optimal Investment and Reinsurance Under the Gamma Process," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 893-923, September.
    16. Meng, Hui & Wei, Li & Zhou, Ming, 2023. "Multiple per-claim reinsurance based on maximizing the Lundberg exponent," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 33-47.

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