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Optimal risk transfer under quantile-based risk measurers

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  • Asimit, Alexandru V.
  • Badescu, Alexandru M.
  • Verdonck, Tim

Abstract

The classical problem of identifying the optimal risk transfer from one insurance company to multiple reinsurance companies is examined under some quantile-based risk measure criteria. We develop a new methodology via a two-stage optimisation procedure which not only allows us to recover some existing results in the literature, but also makes possible the analysis of high-dimensional problems in which the insurance company diversifies its risk with multiple reinsurance counter-parties, where the insurer risk position and the premium charged by the reinsurers are functions of the underlying risk quantile. Closed-form solutions are elaborated for some particular settings, although numerical methods for the second part of our procedure represent viable alternatives for the ease of implementing it in more complex scenarios. Furthermore, we discuss some approaches to obtain more robust results.

Suggested Citation

  • Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:252-265
    DOI: 10.1016/j.insmatheco.2013.05.005
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    Cited by:

    1. 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.
    2. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.
    3. repec:eee:ejores:v:262:y:2017:i:2:p:720-732 is not listed on IDEAS
    4. Payandeh Najafabadi, Amir T. & Bazaz, Ali Panahi, 2016. "An optimal co-reinsurance strategy," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 149-155.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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