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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
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    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.
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