IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v59y2016icp182-195.html
   My bibliography  Save this article

Optimal reinsurance policies with two reinsurers in continuous time

Author

Listed:
  • Meng, Hui
  • Zhou, Ming
  • Siu, Tak Kuen

Abstract

An optimal reinsurance problem of an insurer is studied in a continuous-time model, where insurance risk is partly transferred to two reinsurers, one adopting the expected-value premium principle and another one using the variance premium principle. The insurer aims to select an optimal reinsurance arrangement to minimize the probability of ruin. To provide an easy-to-implement solution to the problem, (semi)-explicit expressions for the optimal reinsurance strategies as well as the minimal ruin probabilities are derived for several claims distributions. Numerical studies including a real-data example based on the Danish fire insurance losses are provided to illustrate the solution of the problem. Our empirical results based on the Danish data reveal that the heavy-right-tailedness of claims distributions has a significant impact on the optimal reinsurance strategies and has a quite pronounced impact on the residual risk described by the minimal ruin probability.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecmode:v:59:y:2016:i:c:p:182-195
    DOI: 10.1016/j.econmod.2016.07.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999316301924
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2016.07.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Meng, Hui & Siu, Tak Kuen & Yang, Hailiang, 2013. "Optimal dividends with debts and nonlinear insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 110-121.
    4. Marie Laure Delignette-Muller & Christophe Dutang, 2015. "fitdistrplus : An R Package for Fitting Distributions," Post-Print hal-01616147, HAL.
    5. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    6. Chi, Yichun, 2012. "Optimal reinsurance under variance related premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 310-321.
    7. S. David Promislow & Virginia Young, 2005. "Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 110-128.
    8. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    9. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    10. 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.
    11. 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.
    12. Delignette-Muller, Marie Laure & Dutang, Christophe, 2015. "fitdistrplus: An R Package for Fitting Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i04).
    13. de Lourdes Centeno, Maria, 2005. "Dependent risks and excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 229-238, October.
    14. Hipp, Christian & Taksar, Michael, 2010. "Optimal non-proportional reinsurance control," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 246-254, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Lv & Shen, Yang & Su, Jianxi, 2020. "A continuous-time theory of reinsurance chains," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 129-146.
    2. 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.
    3. Liyuan Lin & Fangda Liu & Jingzhen Liu abd Luyang Yu, 2023. "The optimal reinsurance strategy with price-competition between two reinsurers," Papers 2305.00509, arXiv.org.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Xiaoqing Liang & Zbigniew Palmowski, 2016. "A note on optimal expected utility of dividend payments with proportional reinsurance," Papers 1605.06849, arXiv.org, revised May 2017.
    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. 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.
    5. 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.
    6. Sarra Ghaddab & Manel Kacem & Christian Peretti & Lotfi Belkacem, 2023. "Extreme severity modeling using a GLM-GPD combination: application to an excess of loss reinsurance treaty," Empirical Economics, Springer, vol. 65(3), pages 1105-1127, September.
    7. 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.
    8. 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.
    9. 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.
    10. Meng, Hui & Li, Shuanming & Jin, Zhuo, 2015. "A reinsurance game between two insurance companies with nonlinear risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 91-97.
    11. Xue, Xiaole & Wei, Pengyu & Weng, Chengguo, 2019. "Derivatives trading for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 40-53.
    12. 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.
    13. 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.
    14. 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.
    15. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    16. 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.
    17. 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.
    18. Linlin Tian & Lihua Bai, 2020. "Minimizing the Ruin Probability under the Sparre Andersen Model," Papers 2004.08124, arXiv.org.
    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. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecmode:v:59:y:2016:i:c:p:182-195. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.