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Optimal Reinsurance with Heterogeneous Reference Probabilities

Author

Listed:
  • Tim J. Boonen

    (Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, Amsterdam 1018 WB, The Netherlands)

Abstract
This paper studies the problem of optimal reinsurance contract design. We let the insurer use dual utility, and the premium is an extended Wang’s premium principle. The novel contribution is that we allow for heterogeneity in the beliefs regarding the underlying probability distribution. We characterize layer-reinsurance as an optimal reinsurance contract. Moreover, we characterize layer-reinsurance as optimal contracts when the insurer faces costs of holding regulatory capital. We illustrate this in cases where both firms use the Value-at-Risk or the conditional Value-at-Risk.

Suggested Citation

  • Tim J. Boonen, 2016. "Optimal Reinsurance with Heterogeneous Reference Probabilities," Risks, MDPI, vol. 4(3), pages 1-11, July.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:3:p:26-:d:73448
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    References listed on IDEAS

    as
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    Cited by:

    1. Chi, Yichun & Zhuang, Sheng Chao, 2020. "Optimal insurance with belief heterogeneity and incentive compatibility," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 104-114.
    2. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance with belief heterogeneity," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 79-91.
    3. Felix-Benedikt Liebrich, 2024. "Risk sharing under heterogeneous beliefs without convexity," Finance and Stochastics, Springer, vol. 28(4), pages 999-1033, October.
    4. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    5. Boonen, Tim J. & Ghossoub, Mario, 2019. "On the existence of a representative reinsurer under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 209-225.
    6. Peng Liu & Andreas Tsanakas & Yunran Wei, 2024. "Risk sharing with Lambda value at risk under heterogeneous beliefs," Papers 2408.03147, arXiv.org, revised Sep 2024.
    7. Felix-Benedikt Liebrich, 2021. "Risk sharing under heterogeneous beliefs without convexity," Papers 2108.05791, arXiv.org, revised May 2022.
    8. Boonen, Tim J. & Jiang, Wenjun, 2022. "A marginal indemnity function approach to optimal reinsurance under the Vajda condition," European Journal of Operational Research, Elsevier, vol. 303(2), pages 928-944.
    9. 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.
    10. Jiang, Wenjun & Ren, Jiandong & Yang, Chen & Hong, Hanping, 2019. "On optimal reinsurance treaties in cooperative game under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 173-184.
    11. 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.
    12. Boonen, Tim J. & Ghossoub, Mario, 2021. "Optimal reinsurance with multiple reinsurers: Distortion risk measures, distortion premium principles, and heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 23-37.

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