IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1912.04175.html
   My bibliography  Save this paper

How much is optimal reinsurance degraded by error?

Author

Listed:
  • Yinzhi Wang
  • Erik B{o}lviken

Abstract

The literature on optimal reinsurance does not deal with how much the effectiveness of such solutions is degraded by errors in parameters and models. The issue is investigated through both asymptotics and numerical studies. It is shown that the rate of degradation is often $O(1/n)$ as the sample size $n$ of historical observations becomes infinite. Criteria based on Value at Risk are exceptions that may achieve only $O(1/\sqrt{n})$. These theoretical results are supported by numerical studies. A Bayesian perspective on how to integrate risk caused by parameter error is offered as well.

Suggested Citation

  • Yinzhi Wang & Erik B{o}lviken, 2019. "How much is optimal reinsurance degraded by error?," Papers 1912.04175, arXiv.org.
    • Handle: RePEc:arx:papers:1912.04175
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1912.04175
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
    2. Erik B{o}lviken & Yinzhi Wang, 2019. "Optimal reinsurance for risk over surplus ratios," Papers 1912.04086, arXiv.org.
    3. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
    4. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    5. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
    6. Yichun Chi & X. Sheldon Lin & Ken Seng Tan, 2017. "Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 417-432, July.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    8. Guerra, Manuel & de Lourdes Centeno, Maria, 2008. "Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 529-539, April.
    9. Young, Virginia R., 1999. "Optimal insurance under Wang's premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 109-122, November.
    10. Jianfa Cong & Ken Seng Tan, 2016. "Optimal VaR-based risk management with reinsurance," Annals of Operations Research, Springer, vol. 237(1), pages 177-202, February.
    11. Chi, Yichun & Tan, Ken Seng, 2011. "Optimal Reinsurance under VaR and CVaR Risk Measures: a Simplified Approach," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 487-509, November.
    12. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
    13. Jianfa Cong & Ken Tan, 2016. "Optimal VaR-based risk management with reinsurance," Annals of Operations Research, Springer, vol. 237(1), pages 177-202, February.
    14. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    15. Marek Kaluszka & Andrzej Okolewski, 2008. "An Extension of Arrow's Result on Optimal Reinsurance Contract," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 275-288, June.
    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. Erik B{o}lviken & Yinzhi Wang, 2019. "Optimal reinsurance for risk over surplus ratios," Papers 1912.04086, arXiv.org.

    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. Chi, Yichun & Liu, Fangda, 2017. "Optimal insurance design in the presence of exclusion clauses," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 185-195.
    2. Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 179-189.
    3. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    4. Lu, ZhiYi & Meng, LiLi & Wang, Yujin & Shen, Qingjie, 2016. "Optimal reinsurance under VaR and TVaR risk measures in the presence of reinsurer’s risk limit," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 92-100.
    5. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    6. Jianfa Cong & Ken Tan, 2016. "Optimal VaR-based risk management with reinsurance," Annals of Operations Research, Springer, vol. 237(1), pages 177-202, February.
    7. Yuxia Huang & Chuancun Yin, 2018. "A unifying approach to constrained and unconstrained optimal reinsurance," Papers 1807.06892, arXiv.org.
    8. Zhu, Yunzhou & Chi, Yichun & Weng, Chengguo, 2014. "Multivariate reinsurance designs for minimizing an insurer’s capital requirement," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 144-155.
    9. Jianfa Cong & Ken Seng Tan, 2016. "Optimal VaR-based risk management with reinsurance," Annals of Operations Research, Springer, vol. 237(1), pages 177-202, February.
    10. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.
    11. Asimit, Alexandru V. & Chi, Yichun & Hu, Junlei, 2015. "Optimal non-life reinsurance under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 227-237.
    12. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2021. "Optimal reinsurance with multiple reinsurers: Competitive pricing and coalition stability," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 302-319.
    13. Albrecher, Hansjörg & Cani, Arian, 2019. "On randomized reinsurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 67-78.
    14. Asimit, Alexandru V. & Badescu, Alexandru M. & Cheung, Ka Chun, 2013. "Optimal reinsurance in the presence of counterparty default risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 690-697.
    15. Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, vol. 4(4), pages 1-12, December.
    16. Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, vol. 1(2), pages 1-12, August.
    17. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    18. Zheng, Yanting & Cui, Wei, 2014. "Optimal reinsurance with premium constraint under distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 109-120.
    19. Junhong Du & Zhiming Li & Lijun Wu, 2019. "Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1133-1151, March.
    20. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1912.04175. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.