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The Reinsurer's Monopoly and the Bowley Solution

Author

Listed:
  • Chan, Fung-Yee
  • Gerber, Hans U.

Abstract

The reinsurer has a monopoly in the following sense: He will select a random variable P that determines the reinsurance premiums. The first insurer can purchase a payment of R (a random variable) for a premium of π = E[PR]. For known P, the first insurer chooses R to maximize his expected utility. Knowing this, i.e., the demand for reinsurance as a function of P, the reinsurer chooses P to maximize his utility. The resulting pair (P, R) is called the Bowley solution. Assuming exponential, quadratic and/or linear utility functions, some explicit results are obtained.

Suggested Citation

  • Chan, Fung-Yee & Gerber, Hans U., 1985. "The Reinsurer's Monopoly and the Bowley Solution," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 141-148, November.
    • Handle: RePEc:cup:astinb:v:15:y:1985:i:02:p:141-148_00
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    Citations

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    Cited by:

    1. Li, Danping & Young, Virginia R., 2021. "Bowley solution of a mean–variance game in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 35-43.
    2. Tim J. Boonen & Wenyuan Li & Zixiao Quan, 2025. "Monopoly Pricing of Weather Index Insurance," Papers 2512.01623, arXiv.org.
    3. Mario Ghossoub & Jesse Hall & David Saunders, 2023. "Maximum Spectral Measures of Risk with Given Risk Factor Marginal Distributions," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 1158-1182, May.
    4. 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.
    5. Zhu, Michael B. & Ghossoub, Mario & Boonen, Tim J., 2023. "Equilibria and efficiency in a reinsurance market," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 24-49.
    6. Anthropelos, Michail & Boonen, Tim J., 2020. "Nash equilibria in optimal reinsurance bargaining," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 196-205.
    7. Chi, Yichun & Tan, Ken Seng & Zhuang, Sheng Chao, 2020. "A Bowley solution with limited ceded risk for a monopolistic reinsurer," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 188-201.
    8. 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.
    9. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2025. "Co-opetition in reinsurance markets: When Pareto meets Stackelberg and Nash," Insurance: Mathematics and Economics, Elsevier, vol. 125(C).
    10. Li, Danping & Young, Virginia R., 2022. "Stackelberg differential game for reinsurance: Mean-variance framework and random horizon," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 42-55.
    11. Mario Ghossoub & Michael B. Zhu & Wing Fung Chong, 2024. "Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures," Papers 2409.05103, arXiv.org.
    12. Li, Dongchen & Zeng, Yan & Zhao, Yixing, 2025. "The impact of intermediaries on insurance demand and pricing," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 143-156.
    13. Ziyue Shi & David Landriault & Fangda Liu, 2024. "Performance-based variable premium scheme and reinsurance design," Papers 2412.01704, arXiv.org, revised Jul 2025.
    14. Tim J. Boonen & Kenneth Tsz Hin Ng & Tak Wa Ng & Thai Nguyen, 2026. "Pareto and Bowley Reinsurance Games in Peer-to-Peer Insurance," Papers 2602.14223, arXiv.org.
    15. Ghossoub, Mario & Zhu, Michael B., 2024. "Stackelberg equilibria with multiple policyholders," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 189-201.
    16. Maria Andraos & Mario Ghossoub & Bin Li & Benxuan Shi, 2026. "Stackelberg Equilibria in Monopoly Insurance Markets with Probability Weighting," Papers 2602.16401, arXiv.org.
    17. Bensalem, Sarah & Santibáñez, Nicolás Hernández & Kazi-Tani, Nabil, 2020. "Prevention efforts, insurance demand and price incentives under coherent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 369-386.
    18. Ghossoub, Mario & Li, Bin & Shi, Benxuan, 2025. "Bowley-optimal convex-loaded premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 121(C), pages 157-180.
    19. Boonen, Tim J. & Ghossoub, Mario, 2023. "Bowley vs. Pareto optima in reinsurance contracting," European Journal of Operational Research, Elsevier, vol. 307(1), pages 382-391.
    20. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    21. 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.

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