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q-Credibility

Author

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  • Olivier Le Courtois

    (EM - EMLyon Business School)

Abstract

This article extends uniform exposure credibility theory by making quadratic adjustments that take into account the squared values of past observations. This approach amounts to introducing non-linearities in the framework, or to considering higher order cross moments in the computations. We first describe the full parametric approach and, for illustration, we examine the Poisson-gamma and Poisson-Pareto cases. Then, we look at the non-parametric approach where premiums can only be estimated from data and no type of distribution is postulated. Finally, we examine the semi-parametric approach where the conditional distribution is Poisson but the unconditional distribution is unknown. For all of these approaches, the mean square error is, by construction, smaller in the q-credibility framework than in the standard framework.

Suggested Citation

  • Olivier Le Courtois, 2020. "q-Credibility," Post-Print hal-02525182, HAL.
    • Handle: RePEc:hal:journl:hal-02525182
    Note: View the original document on HAL open archive server: https://hal.science/hal-02525182
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    References listed on IDEAS

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    1. De Vylder, Fl., 1978. "Parameter Estimation in Credibility Theory," ASTIN Bulletin, Cambridge University Press, vol. 10(1), pages 99-112, May.
    2. Liang Hong & Ryan Martin, 2017. "A Flexible Bayesian Nonparametric Model for Predicting Future Insurance Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(2), pages 228-241, April.
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