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Bonus--malus systems with different claim types and varying deductibles

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  • Olena Ragulina

Abstract

The paper deals with bonus-malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus-malus scale and the types of the reported claims. We introduce such bonus-malus systems and study their basic properties. In particular, we investigate when it is possible to introduce varying deductibles, what restrictions we have and how we can do this. Moreover, we deal with the special case where varying deductibles are applied to the claims reported by policyholders occupying the highest level in the bonus-malus scale and consider two allocation principles for the deductibles. Finally, numerical illustrations are presented.

Suggested Citation

  • Olena Ragulina, 2017. "Bonus--malus systems with different claim types and varying deductibles," Papers 1707.00917, arXiv.org.
  • Handle: RePEc:arx:papers:1707.00917
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    References listed on IDEAS

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    1. Dionne, G & Vanasse, C, 1992. "Automobile Insurance Ratemaking in the Presence of Asymmetrical Information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(2), pages 149-165, April-Jun.
    2. repec:cup:astinb:v:19:y:1989:i:02:p:199-212_00 is not listed on IDEAS
    3. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems using Finite Mixture Models," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 44(02), pages 417-444, May.
    4. Pinquet, Jean, 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 28(02), pages 205-220, November.
    5. Pinquet, Jean, 1997. "Allowance for Cost of Claims in Bonus-Malus Systems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(01), pages 33-57, May.
    6. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems using finite mixture models," LSE Research Online Documents on Economics 70919, London School of Economics and Political Science, LSE Library.
    7. Holtan, Jon, 1994. "Bonus Made Easy," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(01), pages 61-74, May.
    8. Mahmoudvand, Rahim & Hassani, Hossein, 2009. "Generalized Bonus-Malus Systems with a Frequency and a Severity Component on an Individual Basis in Automobile Insurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 39(01), pages 307-315, May.
    9. Sandra Pitrebois & Michel Denuit & Jean-François Walhin, 2006. "Multi-Event Bonus-Malus Scales," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(3), pages 517-528.
    10. Pitrebois, Sandra & Walhin, Jean-François & Denuit, Michel, 2005. "Bonus-malus Systems with Varying Deductibles," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 35(01), pages 261-274, May.
    11. Lemaire, Jean & Zi, Hongmin, 1994. "High Deductibles instead of Bonus-Malus: Can it Work?," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(01), pages 75-86, May.
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