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An approach to merit rating by means of autoregressive sequences

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  • Martinek, László
  • Arató, N. Miklós

Abstract

A posteriori ratemaking is widely applied in the premium calculation of property and casualty products, particularly in third-party automobile insurance, which usually uses a bonus–malus system for premium adjustment. The present paper suggests an alternative to common frameworks that are designed as random walks on graphs of mostly finite states representing premium levels. The proposed premium calculation model is governed by the policyholder’s claim history through a recursive equation. This new autoregressive scheme is structurally different from the ones in use. Relevant metrics that measure the system’s optimality are evaluated, partially in analytical form. Through a comparison with existing models and parameterisation from real-life data, the new model is put into context and its practical relevance is investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:85:y:2019:i:c:p:205-217
    DOI: 10.1016/j.insmatheco.2019.01.008
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    References listed on IDEAS

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    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. Coene, Geert & Doray, Louis G., 1996. "A financially Balanced Bonus/Malus System," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 107-116, May.
    4. 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.
    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. Arthur Charpentier & Arthur David & Romuald Elie, 2017. "Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains," Risks, MDPI, vol. 5(4), pages 1-17, November.
    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. Arthur Charpentier & Arthur David & Romuald Elie, 2016. "Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains," Working Papers hal-01326798, HAL.
    9. 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.
    10. Loimaranta, K., 1972. "Some asymptotic properties of bonus systems," ASTIN Bulletin, Cambridge University Press, vol. 6(3), pages 233-245, May.
    11. Lemaire, Jean & Zi, Hongmin, 1994. "A Comparative Analysis of 30 Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 287-309, November.
    12. Søren Asmussen, 2014. "Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction," Risks, MDPI, vol. 2(1), pages 1-25, March.
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    More about this item

    Keywords

    Autoregressive processes; bonus–malus systems; Model optimisation; Experience rating; Financial equilibrium;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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