IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v61y2015icp255-263.html
   My bibliography  Save this article

Optimal relativities and transition rules of a bonus–malus system

Author

Listed:
  • Tan, Chong It
  • Li, Jackie
  • Li, Johnny Siu-Hang
  • Balasooriya, Uditha

Abstract

When a bonus–malus system with a single set of optimal relativities and a set of simple transition rules is implemented, two inadequacy scenarios are induced because all policyholders are subject to the same a posteriori premium relativities (level transitions) independent of their a priori characteristics (current levels occupied). In this paper we propose a new objective function in the determination of optimal relativities that directly incorporates the a priori expected claim frequencies to partially address one of the inadequacy scenarios. We derive the analytical solution for the optimal relativities under a financial equilibrium constraint. Furthermore, we introduce a metric called effectiveness of transition rules to compare the different specifications of transition rules. We also argue that varying transition rules which are more flexible in addressing the other inadequacy scenario may be more effective than their corresponding simple rules.

Suggested Citation

  • Tan, Chong It & Li, Jackie & Li, Johnny Siu-Hang & Balasooriya, Uditha, 2015. "Optimal relativities and transition rules of a bonus–malus system," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 255-263.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:255-263
    DOI: 10.1016/j.insmatheco.2015.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668715000153
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2015.02.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    2. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems Using Finite Mixture Models," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 417-444, May.
    3. Pinquet, Jean, 1997. "Allowance for Cost of Claims in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 33-57, May.
    4. Taylor, Greg, 1997. "Setting a Bonus-Malus Scale in the Presence of other Rating Factors," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 319-327, November.
    5. 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.
    6. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
    7. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    8. J.F. Walhin, & Paris, J., 1999. "Using Mixed Poisson Processes in Connection with Bonus-Malus Systems1," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 81-99, May.
    9. Frangos, Nicholas E. & Vrontos, Spyridon D., 2001. "Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 1-22, May.
    10. 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, Cambridge University Press, vol. 39(1), pages 307-315, May.
    11. Tremblay, Luc, 1992. "Using the Poisson Inverse Gaussian in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 22(1), pages 97-106, May.
    12. Pitrebois, Sandra & Denuit, Michel & Walhin, Jean-François, 2003. "Setting a Bonus-Malus Scale in the Presence of Other Rating Factors: Taylor's Work Revisited," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 419-436, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martinek, László & Arató, N. Miklós, 2019. "An approach to merit rating by means of autoregressive sequences," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 205-217.
    2. Oh, Rosy & Lee, Kyung Suk & Park, Sojung C. & Ahn, Jae Youn, 2020. "Double-counting problem of the bonus–malus system," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 141-155.
    3. Park, Sojung C. & Kim, Joseph H.T. & Ahn, Jae Youn, 2018. "Does hunger for bonuses drive the dependence between claim frequency and severity?," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 32-46.
    4. Tan, Chong It, 2016. "Varying transition rules in bonus–malus systems: From rules specification to determination of optimal relativities," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 134-140.

    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. Tan, Chong It, 2016. "Varying transition rules in bonus–malus systems: From rules specification to determination of optimal relativities," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 134-140.
    2. George Tzougas, 2020. "EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking," Risks, MDPI, vol. 8(3), pages 1-23, September.
    3. Tzougas, George, 2020. "EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking," LSE Research Online Documents on Economics 106539, London School of Economics and Political Science, LSE Library.
    4. Olena Ragulina, 2017. "Bonus--malus systems with different claim types and varying deductibles," Papers 1707.00917, arXiv.org.
    5. Tzougas, George & Hoon, W. L. & Lim, J. M., 2019. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking," LSE Research Online Documents on Economics 101728, London School of Economics and Political Science, LSE Library.
    6. Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
    7. Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2019. "Insurance ratemaking using the Exponential-Lognormal regression model," LSE Research Online Documents on Economics 101729, London School of Economics and Political Science, LSE Library.
    8. Mahmoudvand Rahim & Tan Chong It & Abbasi Narges, 2017. "Adjusting the Premium Relativities in a Bonus-Malus System: An Integrated Approach Using the First Claim Time and the Number of Claims," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 11(2), pages 1-19, July.
    9. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2018. "Bonus-Malus systems with two component mixture models arising from different parametric families," LSE Research Online Documents on Economics 84301, London School of Economics and Political Science, LSE Library.
    10. Tzougas, George & Karlis, Dimitris & Frangos, Nicholas, 2017. "Confidence intervals of the premiums of optimal Bonus Malus Systems," LSE Research Online Documents on Economics 70926, London School of Economics and Political Science, LSE Library.
    11. Martinek, László & Arató, N. Miklós, 2019. "An approach to merit rating by means of autoregressive sequences," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 205-217.
    12. Yang Lu, 2019. "Flexible (panel) regression models for bivariate count–continuous data with an insurance application," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1503-1521, October.
    13. 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.
    14. Oh, Rosy & Lee, Kyung Suk & Park, Sojung C. & Ahn, Jae Youn, 2020. "Double-counting problem of the bonus–malus system," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 141-155.
    15. Verschuren, Robert Matthijs, 2022. "Frequency-severity experience rating based on latent Markovian risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 379-392.
    16. 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.
    17. 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.
    18. Lee, Woojoo & Kim, Jeonghwan & Ahn, Jae Youn, 2020. "The Poisson random effect model for experience ratemaking: Limitations and alternative solutions," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 26-36.
    19. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2018. "Multivariate Credibility in Bonus-Malus Systems Distinguishing between Different Types of Claims," Risks, MDPI, vol. 6(2), pages 1-11, April.
    20. David Mihaela & Jemna Dănuţ-Vasile, 2015. "Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models," Scientific Annals of Economics and Business, Sciendo, vol. 62(2), pages 151-168, 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:eee:insuma:v:61:y:2015:i:c:p:255-263. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.