IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v59y2014icp109-120.html
   My bibliography  Save this article

Optimal reinsurance with premium constraint under distortion risk measures

Author

Listed:
  • Zheng, Yanting
  • Cui, Wei

Abstract

Recently distortion risk measure has been an interesting tool for the insurer to reflect its attitude toward risk when forming the optimal reinsurance strategy. Under the distortion risk measure, this paper discusses the reinsurance design with unbinding premium constraint and the ceded loss function in a general feasible region which requiring the retained loss function to be increasing and left-continuous. Explicit solution of the optimal reinsurance strategy is obtained by introducing a premium-adjustment function. Our result has the form of layer reinsurance with the mixture of normal reinsurance strategies in each layer. Finally, to illustrate the applicability of our results, we derive the optimal reinsurance solutions with premium constraint under two special distortion risk measures—VaR and TVaR.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:109-120
    DOI: 10.1016/j.insmatheco.2014.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668714001140
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2014.08.010?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. Zhu, Yunzhou & Zhang, Lixin & Zhang, Yi, 2013. "Optimal reinsurance under the Haezendonck risk measure," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1111-1116.
    2. Promislow, S.David & Young, Virginia R., 2005. "Unifying framework for optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 347-364, June.
    3. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
    4. 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.
    5. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 93-112, May.
    6. Zhou, Chunyang & Wu, Wenfeng & Wu, Chongfeng, 2010. "Optimal insurance in the presence of insurer's loss limit," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 300-307, April.
    7. 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.
    8. Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 179-189.
    9. 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.
    10. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
    11. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
    12. Lu, ZhiYi & Liu, LePing & Meng, ShengWang, 2013. "Optimal reinsurance with concave ceded loss functions under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 46-51.
    13. 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.
    14. 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.
    15. Gajek, Leslaw & Zagrodny, Dariusz, 2000. "Insurer's optimal reinsurance strategies," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 105-112, August.
    16. Sung, K.C.J. & Yam, S.C.P. & Yung, S.P. & Zhou, J.H., 2011. "Behavioral optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 418-428.
    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. Martin Eling & Ruo Jia, 2017. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 20(1), pages 63-77, March.
    2. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2016. "The role of a representative reinsurer in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 196-204.
    3. Asimit, Alexandru V. & Cheung, Ka Chun & Chong, Wing Fung & Hu, Junlei, 2020. "Pareto-optimal insurance contracts with premium budget and minimum charge constraints," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 17-27.
    4. Zang, Xin & Jiang, Fan & Xia, Chenxi & Yang, Jingping, 2024. "Random distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 51-73.
    5. Cheung, Ka Chun & Phillip Yam, Sheung Chi & Yuen, Fei Lung & Zhang, Yiying, 2020. "Concave distortion risk minimizing reinsurance design under adverse selection," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 155-165.
    6. Yuxia Huang & Chuancun Yin, 2018. "A unifying approach to constrained and unconstrained optimal reinsurance," Papers 1807.06892, arXiv.org.
    7. Cheung, Ka Chun & He, Wanting & Wang, He, 2023. "Multi-constrained optimal reinsurance model from the duality perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 199-214.
    8. 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.
    9. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Jianfa Cong & Ken Tan, 2016. "Optimal VaR-based risk management with reinsurance," Annals of Operations Research, Springer, vol. 237(1), pages 177-202, February.
    5. 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.
    6. 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.
    7. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    8. Yuxia Huang & Chuancun Yin, 2018. "A unifying approach to constrained and unconstrained optimal reinsurance," Papers 1807.06892, arXiv.org.
    9. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    10. Chi, Yichun, 2018. "Insurance choice under third degree stochastic dominance," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 198-205.
    11. Lu, ZhiYi & Liu, LePing & Meng, ShengWang, 2013. "Optimal reinsurance with concave ceded loss functions under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 46-51.
    12. Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, vol. 1(2), pages 1-12, August.
    13. 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.
    14. 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.
    15. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "The optimal insurance under disappointment theories," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 77-90.
    16. 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.
    17. 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.
    18. 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.
    19. Cheung, Ka Chun & Phillip Yam, Sheung Chi & Yuen, Fei Lung & Zhang, Yiying, 2020. "Concave distortion risk minimizing reinsurance design under adverse selection," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 155-165.
    20. 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.

    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:insuma:v:59:y:2014:i:c:p:109-120. 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/505554 .

    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.