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Optimal non-proportional reinsurance control

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  • Hipp, Christian
  • Taksar, Michael

Abstract

This paper deals with the problem of ruin probability minimization under various investment control and reinsurance schemes. We first look at the minimization of ruin probabilities in the models in which the surplus process is a continuous diffusion process in which we employ stochastic control to find the optimal policies for reinsurance and investment. We then focus on the case in which the surplus process is modeled via a classical Lundberg process, i.e. the claims process is compound Poisson. There, the optimal reinsurance policy is derived from the Hamilton-Jacobi-Bellman equation.

Suggested Citation

  • Hipp, Christian & Taksar, Michael, 2010. "Optimal non-proportional reinsurance control," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 246-254, October.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:246-254
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    References listed on IDEAS

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    1. Hipp, Christian & Vogt, Michael, 2003. "Optimal Dynamic XL Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 193-207, November.
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    Cited by:

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    2. Taksar, Michael & Zeng, Xudong, 2011. "Optimal non-proportional reinsurance control and stochastic differential games," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 64-71, January.
    3. Asmussen, Søren & Christensen, Bent Jesper & Thøgersen, Julie, 2019. "Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 92-100.
    4. Michael Preischl & Stefan Thonhauser, 2018. "Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model," Papers 1809.00990, arXiv.org.
    5. Yuan, Yu & Han, Xia & Liang, Zhibin & Yuen, Kam Chuen, 2023. "Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework," European Journal of Operational Research, Elsevier, vol. 311(2), pages 581-595.
    6. Nabil Kazi-Tani, 2018. "Inf-Convolution of Choquet Integrals and Applications in Optimal Risk Transfer," Working Papers hal-01742629, HAL.
    7. 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.
    8. Arian Cani & Stefan Thonhauser, 2017. "An optimal reinsurance problem in the Cramér–Lundberg model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 179-205, April.
    9. Wujun Lv & Linlin Tian & Xiaoyi Zhang, 2023. "Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence," Mathematics, MDPI, vol. 11(13), pages 1-20, July.
    10. 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.
    11. 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.
    12. Jang, Bong-Gyu & Kim, Kyeong Tae, 2015. "Optimal reinsurance and asset allocation under regime switching," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 37-47.
    13. 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.
    14. 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.
    15. Linlin Tian & Lihua Bai, 2020. "Minimizing the Ruin Probability under the Sparre Andersen Model," Papers 2004.08124, arXiv.org.
    16. Preischl, M. & Thonhauser, S., 2019. "Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 82-91.
    17. Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    18. 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.
    19. Zhang, Xin & Meng, Hui & Zeng, Yan, 2016. "Optimal investment and reinsurance strategies for insurers with generalized mean–variance premium principle and no-short selling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 125-132.
    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. 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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