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Characterizations of optimal reinsurance treaties: a cost-benefit approach

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  • Ka Chun Cheung
  • Ambrose Lo

Abstract

This article investigates optimal reinsurance treaties minimizing an insurer’s risk-adjusted liability, which encompasses a risk margin quantified by distortion risk measures. Via the introduction of a transparent cost-benefit argument, we extend the results in Cui et al. [Cui, W., Yang, J. & Wu, L. (2013). Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles. Insurance: Mathematics and Economics 53, 74–85] and provide full characterizations on the set of optimal reinsurance treaties within the class of non-decreasing, 1-Lipschitz functions. Unlike conventional studies, our results address the issue of (non-)uniqueness of optimal solutions and indicate that ceded loss functions beyond the traditional insurance layers can be optimal in some cases. The usefulness of our novel cost-benefit approach is further demonstrated by readily solving the dual problem of minimizing the reinsurance premium while maintaining the risk-adjusted liability below a fixed tolerance level.

Suggested Citation

  • Ka Chun Cheung & Ambrose Lo, 2017. "Characterizations of optimal reinsurance treaties: a cost-benefit approach," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(1), pages 1-28, January.
    • Handle: RePEc:taf:sactxx:v:2017:y:2017:i:1:p:1-28
    DOI: 10.1080/03461238.2015.1054303
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    Cited by:

    1. Chen, Yanhong & Cheung, Ka Chun & Zhang, Yiying, 2024. "Bowley solution under the reinsurer's default risk," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 36-61.
    2. 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.
    3. Chi, Yichun & Hu, Tao & Huang, Yuxia, 2023. "Optimal risk management with reinsurance and its counterparty risk hedging," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 274-292.
    4. Boonen, Tim J. & Jiang, Wenjun, 2024. "Robust insurance design with distortion risk measures," European Journal of Operational Research, Elsevier, vol. 316(2), pages 694-706.
    5. Tim J. Boonen & Xia Han, 2023. "Optimal insurance with mean-deviation measures," Papers 2312.01813, arXiv.org.

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