On the ordering of credibility factors

Abstract

Traditional credibility analysis of risks in insurance is based on the random effects model, where the heterogeneity across the policyholders is assumed to be time-invariant. One popular extension is the dynamic random effects (or state-space) model. However, while the latter allows for time-varying heterogeneity, its application to the credibility analysis should be conducted with care due to the possibility of negative credibilities per period [see Pinquet (2020a)]. Another important but underexplored topic is the ordering of the credibility factors in a monotonous manner-recent claims ought to have larger weights than the old ones. This paper shows that the ordering of the covariance structure of the random effects in the dynamic random effects model does not necessarily imply that of the credibility factors. Subsequently, we show that the state-space model, with AR(1)-type autocorrelation function, guarantees the ordering of the credibility factors. Simulation experiments and a case study with a real dataset are conducted to show the relevance in insurance applications.

A simple Bayesian state-space model for the collective risk model

“…In the following, we show that the one step-ahead forecasting can be represented as the linear combination of claims with timely ordered weights. Note that, for the pair comparison of the contribution of each claims, it is important to assume the same prior rates (Ahn et al, 2021).…”