On the ordering of credibility factors

Jae Youn Ahn, Himchan Jeong, Yang Lu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 under-explored 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.

Original languageEnglish
Pages (from-to)626-638
Number of pages13
JournalInsurance: Mathematics and Economics
StatePublished - Nov 2021

Bibliographical note

Funding Information:
The authors warmly thank two anonymous referees and the editors for their numerous constructive comments that greatly helped to improve the paper compared to its initial version. Jae Youn Ahn was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government ( 2020R1F1A1A01061202 ). Himchan Jeong was supported by the Simon Fraser University New Faculty Start-up Grant ( NFSG-N000831 ). Yang Lu thanks CNRS (France) for a teaching release grant, Concordia University for a Start-up grant as well as NSERC through a Discovery Grant ( RGPIN-2021-04144 , DGECR-2021-00330 ). The authors wish to thank Prof. Jean Pinquet and Prof. Dong Wan Shin for their comments.

Publisher Copyright:
© 2021 Elsevier B.V.


  • Auto insurance
  • Credibility
  • Dependence
  • Dynamic random effects
  • Posterior ratemaking
  • Time series


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