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q-Credibility

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.
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https://hal.archives-ouvertes.fr/hal-02525182
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Submitted on : Monday, March 30, 2020 - 6:03:26 PM
Last modification on : Sunday, January 10, 2021 - 11:54:32 PM

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Olivier Le Courtois. q-Credibility. Variance, 2020. ⟨hal-02525182⟩

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