TY - JOUR
T1 - On the ordering of credibility factors
AU - Youn Ahn, Jae
AU - Jeong, Himchan
AU - Lu, Yang
N1 - 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.
PY - 2021/11
Y1 - 2021/11
N2 - 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.
AB - 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.
KW - Auto insurance
KW - Credibility
KW - Dependence
KW - Dynamic random effects
KW - Posterior ratemaking
KW - Time series
UR - http://www.scopus.com/inward/record.url?scp=85118840707&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2021.10.005
DO - 10.1016/j.insmatheco.2021.10.005
M3 - Article
AN - SCOPUS:85118840707
SN - 0167-6687
VL - 101
SP - 626
EP - 638
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -