q-Credibility

Abstract

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