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Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles

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  • Cui, Wei
  • Yang, Jingping
  • Wu, Lan

Abstract

Recently the optimal reinsurance strategy concerning the insurer’s risk attitude and the reinsurance premium principle has been an interesting topic. This paper discusses the optimal reinsurance problem with the insurer’s risk measured by distortion risk measure and the reinsurance premium calculated by a general principle including expected premium principle and Wang’s premium principle as its special cases. Explicit solutions of the optimal reinsurance strategy are obtained under the assumption that both the ceded loss and the retained loss are increasing with the initial loss. We present a new method for discussing the optimal problem. Based on our method, one can explain the optimal reinsurance treaty in the view of a balance between the insurer’s risk measure and the reinsurance premium principle.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:74-85
    DOI: 10.1016/j.insmatheco.2013.03.007
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Ambrose Lo, 2016. "How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-16, December.
    2. Balbas de la Corte, Alejandro & Balbas Aparicio, Beatriz & Balbas Aparicio, Raquel & Heras, Antonio, 2014. "Optimal reinsurance under risk and uncertainty," INDEM - Working Paper Business Economic Series id-14-04, Instituto para el Desarrollo Empresarial (INDEM).
    3. repec:eee:insuma:v:80:y:2018:i:c:p:15-28 is not listed on IDEAS
    4. Mario Brandtner, 2016. "Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke," Management Review Quarterly, Springer;Vienna University of Economics and Business, vol. 66(2), pages 75-115, April.
    5. 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.
    6. Christian Biener & Martin Eling & Shailee Pradhan, 2015. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2013 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 18(1), pages 129-141, March.
    7. repec:eee:ejores:v:267:y:2018:i:2:p:778-790 is not listed on IDEAS
    8. 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.
    9. 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.
    10. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel & Heras, Antonio, 2015. "Optimal reinsurance under risk and uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 61-74.
    11. 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.
    12. Tim J. Boonen, 2016. "Optimal Reinsurance with Heterogeneous Reference Probabilities," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-11, July.
    13. Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-12, December.
    14. repec:eee:insuma:v:77:y:2017:i:c:p:24-37 is not listed on IDEAS

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