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Optimal reinsurance designs based on risk measures: a review

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  • Jun Cai
  • Yichun Chi

Abstract

Reinsurance is an effective way for an insurance company to control its risk. How to design an optimal reinsurance contract is not only a key topic in actuarial science, but also an interesting research question in mathematics and statistics. Optimal reinsurance design problems can be proposed from different perspectives. Risk measures as tools of quantitative risk management have been extensively used in insurance and finance. Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic. Different research approaches have been developed and many interesting results have been obtained in this area. These approaches and results have potential applications in future research. In this article, we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.

Suggested Citation

  • Jun Cai & Yichun Chi, 2020. "Optimal reinsurance designs based on risk measures: a review," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 4(1), pages 1-13, July.
    • Handle: RePEc:taf:tstfxx:v:4:y:2020:i:1:p:1-13
    DOI: 10.1080/24754269.2020.1758500
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    Citations

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    Cited by:

    1. Tang, Qihe & Tong, Zhiwei & Xun, Li, 2022. "Portfolio risk analysis of excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 91-110.
    2. Benjamin Avanzi & Hayden Lau & Mogens Steffensen, 2022. "Optimal reinsurance design under solvency constraints," Papers 2203.16108, arXiv.org, revised Jun 2023.
    3. Qiuqi Wang & Ruodu Wang & Ricardas Zitikis, 2021. "Risk measures induced by efficient insurance contracts," Papers 2109.00314, arXiv.org, revised Sep 2021.
    4. Wang, Qiuqi & Wang, Ruodu & Zitikis, Ričardas, 2022. "Risk measures induced by efficient insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 56-65.
    5. Chi, Yichun & Liu, Fangda, 2021. "Enhancing an insurer's expected value by reinsurance and external financing," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 466-484.
    6. Liang, Xiaoqing & Jiang, Wenjun & Zhang, Yiying, 2023. "Optimal insurance design under mean-variance preference with narrow framing," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 59-79.
    7. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2023. "Optimal moral-hazard-free reinsurance under extended distortion premium principles," Papers 2304.08819, arXiv.org.
    8. Shen, Yang & Zou, Bin, 2021. "Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 68-80.
    9. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2023. "Reinsurance games with two reinsurers: Tree versus chain," European Journal of Operational Research, Elsevier, vol. 310(2), pages 928-941.
    10. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    11. Vincent, Léonard & Albrecher, Hansjörg & Krvavych, Yuriy, 2021. "Structured reinsurance deals with reference to relative market performance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 125-139.
    12. Jean-Gabriel Lauzier, 2021. "Insurance design and arson-type risks," Papers 2112.06817, arXiv.org.

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