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On a class of measures of dispersion with application to optimal reinsurance

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  • Ohlin, Jan

Abstract

In this paper we will investigate the following reinsurance problem: An insurer, whose total claims for a certain period may be regarded as a random variable x with expected value Ex = m, wishes to cede part of his business to a reinsurer. A reinsurance treaty will consist of rule for the division of x between the two parties. For any observed value of x it should define uniquely what amount should be borne by the ceding insurer. The amount borne by the reinsurer is then simply the remaining part of x.We shall assume that the insurer has already decided how much of his business he wishes to cede, in the sense that he wants to retain a part of the total risk with expected value m — c, where c is a fixed constant, o

Suggested Citation

  • Ohlin, Jan, 1969. "On a class of measures of dispersion with application to optimal reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 5(2), pages 249-266, May.
    • Handle: RePEc:cup:astinb:v:5:y:1969:i:02:p:249-266_00
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    Cited by:

    1. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    2. Juan-José Ganuza & José S. Penalva, 2005. "On Information and Competition in Private Value Auctions," Working Papers 158, Barcelona School of Economics.
    3. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.
    4. Chi, Yichun & Zhou, Xun Yu & Zhuang, Sheng Chao, 2024. "Variance insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 62-82.
    5. Magnus Carlehed, 2023. "A Model for Risk Adjustment (IFRS 17) for Surrender Risk in Life Insurance," Risks, MDPI, vol. 11(3), pages 1-22, March.
    6. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    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. Chi, Yichun, 2018. "Insurance choice under third degree stochastic dominance," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 198-205.
    9. Guerra, Manuel & de Lourdes Centeno, Maria, 2008. "Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 529-539, April.
    10. 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.
    11. Kaluszka, Marek, 2004. "An extension of Arrow's result on optimality of a stop loss contract," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 527-536, December.
    12. Chi, Yichun & Liu, Fangda, 2017. "Optimal insurance design in the presence of exclusion clauses," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 185-195.
    13. Epebinu, Abayomi Dennis & Szostok, Tomasz, 2024. "Inequalities for fractional integral with the use of stochastic orderings," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    14. Abhishek, Vineet & Hajek, Bruce & Williams, Steven R., 2013. "Auctions with a profit sharing contract," Games and Economic Behavior, Elsevier, vol. 77(1), pages 247-270.
    15. Muller, Alfred, 1996. "Orderings of risks: A comparative study via stop-loss transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(3), pages 215-222, April.
    16. 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.
    17. Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 179-189.
    18. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    19. Abhishek, Vineet & Hajek, Bruce & Williams, Steven R., 2015. "On bidding with securities: Risk aversion and positive dependence," Games and Economic Behavior, Elsevier, vol. 90(C), pages 66-80.
    20. Asimit, Alexandru V. & Chi, Yichun & Hu, Junlei, 2015. "Optimal non-life reinsurance under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 227-237.
    21. Zhu, Yunzhou & Chi, Yichun & Weng, Chengguo, 2014. "Multivariate reinsurance designs for minimizing an insurer’s capital requirement," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 144-155.

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