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On Combining Quota-Share and Excess of Loss

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  • Centeno, Lourdes

Abstract

This paper considers reinsurance retention limits in cases where the cedent has a choice between a pure quota-share treaty, a pure excess of loss treaty or a combination of the two. Our primary aim is to find the combination of retention limits which minimizes the skewness coefficient of the insurer's retained risk subject to constraints on the variance and the expected value of his retained risk. The results are given without specifying precisely how the excess of loss reinsurance premium is calculated. It is also shown that, depending to some extent on the constraint on the variance, the solution to the problem is a pure excess of loss treaty if the excess of loss premium is calculated using the expected value or standard deviation principle but that this need not be true if the variance principle is used.

Suggested Citation

  • Centeno, Lourdes, 1985. "On Combining Quota-Share and Excess of Loss," ASTIN Bulletin, Cambridge University Press, vol. 15(1), pages 49-63, April.
    • Handle: RePEc:cup:astinb:v:15:y:1985:i:01:p:49-63_00
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    Citations

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    Cited by:

    1. Hu, Xiang & Duan, Baige & Zhang, Lianzeng, 2017. "De Vylder approximation to the optimal retention for a combination of quota-share and excess of loss reinsurance with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 48-55.
    2. Kull, Andreas, 2009. "Sharing Risk – An Economic Perspective," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 591-613, November.
    3. Cerqueti, Roy & Foschi, Rachele & Spizzichino, Fabio, 2009. "A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 59-64, August.
    4. Verlaak, Robert & Beirlant, Jan, 2003. "Optimal reinsurance programs: An optimal combination of several reinsurance protections on a heterogeneous insurance portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 381-403, October.
    5. Ladoucette, Sophie A. & Teugels, Jef L., 2006. "Analysis of risk measures for reinsurance layers," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 630-639, June.
    6. Centeno, Maria de Lourdes, 2002. "Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 37-49, February.

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