IDEAS home Printed from https://ideas.repec.org/a/sgh/annals/i37y2015p127-154.html
   My bibliography  Save this article

Merging and aggregation of bonus-malus systems in automobile insurance

Author

Listed:
  • Wojciech Bijak

    (Szkoła Główna Handlowa w Warszawie, Ubezpieczeniowy Fundusz Gwarancyjny)

Abstract

The common practice in automobile insurance (third party liability and comprehensive coverage) is to apply bonus-malus (BM) systems in tariff building. The premium for the insured is defined, among others, on the basis of their claim history. In order to describe BM systems, it is common to use Markov chains, constructed for a single insured person. This work presents a concept of using operations on BM systems to design insurance products for multiple individuals or insurance products where risk is associated with multiple individuals or vehicles. Two operations are presented: merging and aggregation of BM systems. Merging helps to develop an insurance that would cover ever more numerous groups of insured persons or exposure units whereas aggregation helps to treat a particular group as a separate exposure entity (status) exposed to risk in the context of insurance. Insurance with time measured in a discrete way is considered here. An assumption was made that in the case of insurance covering multiple individuals or vehicles, the considered random variables which determine the number of losses are either stochastically independent or have a multivariate Poisson distribution or a multivariate generalised Poisson distribution.

Suggested Citation

  • Wojciech Bijak, 2015. "Merging and aggregation of bonus-malus systems in automobile insurance," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 37, pages 127-154.
  • Handle: RePEc:sgh:annals:i:37:y:2015:p:127-154
    as

    Download full text from publisher

    File URL: http://rocznikikae.sgh.waw.pl/p/roczniki_kae_z37_06.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2006. "Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 25-77, May.
    2. Desjardins, Denise & Dionne, Georges & Pinquet, Jean, 2001. "Experience Rating Schemes for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 81-105, May.
    3. Vernic, Raluca, 2000. "A Multivariate Generalization of the Generalized Poisson Distribution," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 57-67, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Angers, Jean-François & Desjardins, Denise & Dionne, Georges, 2004. "Modèle Bayésien de tarification de l’assurance des flottes de véhicules," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 253-303, Juin-Sept.
    2. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2018. "Modelling And Estimating Individual And Firm Effects With Count Panel Data," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1049-1078, September.
    3. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.
    4. Denise Desjardins & Georges Dionne & Yang Lu, 2023. "Hierarchical random‐effects model for the insurance pricing of vehicles belonging to a fleet," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(2), pages 242-259, March.
    5. Levon Barseghyan & Francesca Molinari & Darcy Steeg Morris & Joshua C. Teitelbaum, 2020. "The Cost of Legal Restrictions on Experience Rating," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 17(1), pages 38-70, March.
    6. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2006. "Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 25-77, May.
    7. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    8. Gathy, Maude & Lefèvre, Claude, 2010. "On the Lagrangian Katz family of distributions as a claim frequency model," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 76-83, August.
    9. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    10. Daiho Uhm & Sunghae Jun, 2022. "Zero-Inflated Patent Data Analysis Using Generating Synthetic Samples," Future Internet, MDPI, vol. 14(7), pages 1-11, July.
    11. Anastasiadis, Simon & Chukova, Stefanka, 2012. "Multivariate insurance models: An overview," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 222-227.
    12. Daniel Sobiecki, 2015. "Experience rating with dependence between MTPL and MOD claims," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 37, pages 269-282.
    13. Asimit, Alexandru V. & Furman, Edward & Vernic, Raluca, 2010. "On a multivariate Pareto distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 308-316, April.
    14. Jean-François Angers & Denise Desjardins & Georges Dionne & Benoit Dostie & François Guertin, 2007. "Poisson Models with Employer-Employee Unobserved Heterogeneity: An Application to Absence Data," Cahiers de recherche 07-02, HEC Montréal, Institut d'économie appliquée.
    15. Övgücan Karadağ Erdemir, 2023. "A Comparative Perspective on Multivariate Modeling of Insurance Compensation Payments with Regression-Based and Copula-Based Models," EKOIST Journal of Econometrics and Statistics, Istanbul University, Faculty of Economics, vol. 0(39), pages 161-171, December.
    16. Bourgeon, Jean-Marc & Picard, Pierre, 2007. "Point-record driving licence and road safety: An economic approach," Journal of Public Economics, Elsevier, vol. 91(1-2), pages 235-258, February.
    17. Asamoah, Kwadwo, 2016. "On the credibility of insurance claim frequency: Generalized count models and parametric estimators," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 339-353.
    18. Dionne, Georges & Desjardins, Denise & Angers, Jean-François, 2021. "Road safety for fleets of vehicles," Working Papers 21-3, HEC Montreal, Canada Research Chair in Risk Management.
    19. Marcin Owczarczuk & Damian Przekop, 2014. "Accidents of company cars. A full service leasing company’s perspective," Applied Econometrics Papers, Department of Applied Econometrics, Warsaw School of Economics, vol. 1(1), pages 39-63.
    20. Indranil Ghosh & Tamara D. H. Cooper, 2023. "On Surprise Indices Related to Univariate Discrete and Continuous Distributions: A Survey," Mathematics, MDPI, vol. 11(14), pages 1-16, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sgh:annals:i:37:y:2015:p:127-154. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Michał Bernardelli (email available below). General contact details of provider: https://edirc.repec.org/data/sgwawpl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.