Variance, Vol. 13, N°2, p. 250–264, 2021

26 Pages Posted: 27 Feb 2015 Last revised: 29 Sep 2021

See all articles by Olivier Le Courtois

Olivier Le Courtois

EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control


This article extends 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 moments in the computations. We first describe a full parametric approach and, for illustration, we examine the Poisson-gamma and Poisson-single Pareto cases. Then, we look at the non-parametric approach where premiums must be estimated based on data only, without postulating any type of distribution. Finally, we examine a semi-parametric approach where the conditional distribution is Poisson but the unconditional distribution is unknown.

Keywords: Credibility, Quadratic Approximation. Parametric, Non-Parametric, Semi-Parametric, Poisson-Gamma, Poisson-Single Pareto, Uniform Exposure

JEL Classification: C11, G22

Suggested Citation

Le Courtois, Olivier Arnaud, q-Credibility. Variance, Vol. 13, N°2, p. 250–264, 2021, Available at SSRN: https://ssrn.com/abstract=2571195 or http://dx.doi.org/10.2139/ssrn.2571195

Olivier Arnaud Le Courtois (Contact Author)

EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control ( email )

23, av. Guy de Collongue
69134 Ecully Cedex

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