q-Credibility

By Olivier Arnaud Le Courtois

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Abstract

This paper extends uniform-exposure credibility theory by making quadratic adjustments that take into account the squared values of past observations. This approach amounts to introducing nonlinearities in the framework, or to consider-ing 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 nonparametric approach, whereby premiums can be estimated only from data and no type of distribution is postulated. Finally, we examine the semiparametric approach, in which the conditional distribution is Poisson but the uncondi-tional distribution is unknown. For all of these approaches, the mean squared error is, by construction, smaller in the q-credibility framework than in the standard framework.

Keywords Credibility, quadratic approximation, parametric, nonparametric, semiparametric, Poisson-Gamma, Poisson-Pareto, uniform exposure

Citation

Le Courtois, Olivier Arnaud, "q-Credibility," Variance 13:2, 2021, pp. 250-264.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.