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On the Maximisation of the Adjustment Coefficient under Proportional Reinsurance

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  • Hald, Morten
  • Schmidli, Hanspeter

Abstract

In this note we consider how to maximise the adjustment coefficient in the case of proportional reinsurance. This complements some work of Waters (1983), where it was shown that there is a unique retention level maximising the adjustment coefficient. The advantage of our method is that only one implicit equation has to be solved.

Suggested Citation

  • Hald, Morten & Schmidli, Hanspeter, 2004. "On the Maximisation of the Adjustment Coefficient under Proportional Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 75-83, May.
    • Handle: RePEc:cup:astinb:v:34:y:2004:i:01:p:75-83_01
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    Cited by:

    1. Preischl, M. & Thonhauser, S., 2019. "Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 82-91.
    2. Yuta Otsuki & Shotaro Yagishita, 2024. "Optimal reinsurance and investment via stochastic projected gradient method based on Malliavin calculus," Papers 2411.05417, arXiv.org.
    3. Michael Preischl & Stefan Thonhauser, 2018. "Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model," Papers 1809.00990, arXiv.org.
    4. Liang, Xiaoqing & Liang, Zhibin & Young, Virginia R., 2020. "Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 128-146.
    5. Arian Cani & Stefan Thonhauser, 2017. "An optimal reinsurance problem in the Cramér–Lundberg model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 179-205, April.
    6. Cossette, Hélène & Marceau, Etienne & Trufin, Julien & Zuyderhoff, Pierre, 2020. "Ruin-based risk measures in discrete-time risk models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 246-261.
    7. El Attar Abderrahim & El Hachloufi Mostafa & Guennoun Zine El Abidine, 2017. "An Inclusive Criterion For An Optimal Choice Of Reinsurance," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 1-22, December.
    8. Meng, Hui & Wei, Li & Zhou, Ming, 2023. "Multiple per-claim reinsurance based on maximizing the Lundberg exponent," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 33-47.

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