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Handbook of Insurance pp 471–485Cite as

Experience Rating in Nonlife Insurance

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Abstract

This chapter presents statistical models which lead to experience rating in insurance. Serial correlation for risk variables can receive endogenous or exogenous explanations. The interpretation retained by actuarial models is exogenous and reflects the positive contagion usually observed for the number of claims. This positive contagion can be explained by the revelation throughout time of a hidden features in the risk distributions. These features are represented by fixed effects which are predicted with a random effects model. This chapter discusses identification issues on the nature of the dynamics of nonlife insurance data. Examples of predictions are given for count data models with a constant or time-varying random effects, one or several equations, and for cost-number models on events.

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Notes

  1. 1.

    Risk reduction applies on frequency rather than severity in most of the economic literature. Hence prevention is of the “self-protection” rather than of the “self-insurance” type, with the Ehrlich–Becker (1972) terminology.

  2. 2.

    Hendel and Lizzeri (2003) mention however term-life insurance contracts in the USA that offer state contingent prices, where low premiums are contingent on the insured showing he is still in good health.

  3. 3.

    Ten years ago, the European Commission sued France, arguing that the bonus-malus system distorted competition. As an answer, French authorities argued that the bonus-malus system did not enforce experience rating. They finally won the case.

  4. 4.

    Kunreuther and Pauly’s model is derived in a no-commitment setting, with myopic consumers (i.e., those who take decisions based on the current contract). Taylor uses a multiperiod approach where the premium is the control variable in the maximization of the customer value. The model also includes an elasticity between the lapse rate and relative prices between the incumbent insurer and its competitors.

  5. 5.

    At the opposite, life and health insurance products are often front-loaded and sometimes heavily without any surrender value as is the case for long-term care insurance. Hendel and Lizzeri (2003) provide an economic analysis of front-loading in term-life insurance in the USA.

  6. 6.

    In most statistical problems, a parameter set has a much smaller dimension than that of the probability set it aims at describing. A parametric approach is a one-to-one map from the parameter set to the probability set. In a semiparametric setting, the parameters are related to constraints on the probabilities.

  7. 7.

    We have \(\sum _{i,t}\widehat{\lambda _{i,t}} =\sum _{i,t}y_{i,t}\) from the orthogonality between the residuals and the intercept.

  8. 8.

    See Zhang (1990) for an approximation of the Fourier transform of the mixing distribution.

  9. 9.

    The independence of the random effects distribution with respect to the regression components can be challenged. This issue is discussed by Boucher and Denuit (2006) and by Bolancé et al. (2008).

  10. 10.

    The parameter set for α is usually a convex cone in \({\mathbb{R}}^{k_{2}}\).

  11. 11.

    The same logic is applied in many point-record driving licenses (where events are traffic violations which are associated to demerit points and where the driving license is suspended once the cumulated demerit points reach a given threshold). In France and in many European countries, all the demerit point is removed after a given period of violation-free driving. In the USA and in Canada, point removal is performed on each traffic offense once a given seniority is reached. The incentive properties of point-record mechanisms are studied by Bourgeon and Picard (2007) and by Dionne et al. (2011).

  12. 12.

    Neyman was far from being a beginner when he wrote this article. He already had published his results on optimal tests with Egon Pearson.

  13. 13.

    The test proposed by Abbring et al. (2003) eliminates unobserved heterogeneity in some unbalanced time-event frameworks.

  14. 14.

    Also, the prediction derived from the INAR(1) model is derived from the number of events restricted to the last period. This is an unpleasant property if events are claims, as all the claims in the past have some predictive ability.

  15. 15.

    Log-normal distributions have, however, thicker tails than the Gamma, as they are of the subexponential type.

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Authors and Affiliations

  1. Université Paris-Ouest Nanterre La Défense and Ecole Polytechnique, Paris, France

    Jean Pinquet

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  1. Jean Pinquet
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Correspondence to Jean Pinquet .

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  1. Finance, HEC Montreal, Montreal, Québec, Canada

    Georges Dionne

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Pinquet, J. (2013). Experience Rating in Nonlife Insurance. In: Dionne, G. (eds) Handbook of Insurance. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0155-1_17

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