A simple Bayesian state-space approach to the collective risk models

Jae Youn Ahn, Himchan Jeong, Yang Lu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, natural disaster forecasting, as well as operational risk in banking regulation. This model, initially designed for cross-sectional data, has recently been adapted to a longitudinal context for both a priori and a posteriori ratemaking, through random effects specifications. However, the random effects are usually assumed to be static due to computational concerns, leading to predictive premiums that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effects processes. The model is based on Bayesian state-space models. It is associated with a simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. A real data application for auto insurance is proposed to show the performance of our method.

Original languageEnglish
Pages (from-to)509-529
Number of pages21
JournalScandinavian Actuarial Journal
Issue number5
StatePublished - 2023

Bibliographical note

Funding Information:
Jae Youn Ahn was partly supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government [grant number 2022R1F1A1064048] and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) [grant number RS-2022-00155966]. Yang Lu thanks NSERC through a discovery grant [grant numbers RGPIN-2021-04144, DGECR-2021-00330]. Himchan Jeong was supported by the Simon Fraser University New Faculty Start-up Grant (NFSG). The authors warmly thank two anonymous referees for their numerous constructive comments that greatly helped to improve the paper compared to its initial version.

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.


  • Dependence
  • conjugate-prior
  • dynamic random effects
  • local-level models
  • posterior ratemaking
  • three-part model


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