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Optimality of general reinsurance contracts under CTE risk measure

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  • Tan, Ken Seng
  • Weng, Chengguo
  • Zhang, Yi
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    Abstract

    By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk. For completeness, we analyze the optimal reinsurance model under both binding and unbinding reinsurance premium constraints. By resorting to the Lagrangian approach based on the concept of directional derivative, explicit and analytical optimal solutions are obtained in each case under some mild conditions. We show that pure stop-loss ceded loss function is always optimal. More interestingly, we demonstrate that ceded loss functions, that are not always non-decreasing, could be optimal. We also show that, in some cases, it is optimal to exhaust the entire reinsurance premium budget to determine the optimal reinsurance, while in other cases, it is rational to spend less than the prescribed reinsurance premium budget.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 49 (2011)
    Issue (Month): 2 (September)
    Pages: 175-187

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    Handle: RePEc:eee:insuma:v:49:y:2011:i:2:p:175-187

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Optimal reinsurance Ceded loss function Conditional tail expectation (CTE) Expectation premium principle Convex analysis Lagrangian method Directional derivative Subdifferential;

    References

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    Cited by:
    1. 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, Elsevier, vol. 52(1), pages 46-51.
    2. Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 53(1), pages 179-189.
    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, Elsevier, vol. 53(1), pages 74-85.
    4. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 52(2), pages 180-189.
    5. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 50(3), pages 446-461.

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