On the ordering of credibility factors

Jae Youn Ahn; Himchan Jeong; Yang Lu

doi:10.1016/j.insmatheco.2021.10.005

On the ordering of credibility factors

Jae Youn Ahn, Himchan Jeong, Yang Lu

Department of Statistics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 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 language	English
Pages (from-to)	626-638
Number of pages	13
Journal	Insurance: Mathematics and Economics
Volume	101
DOIs	https://doi.org/10.1016/j.insmatheco.2021.10.005
State	Published - 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.

Keywords

Auto insurance
Credibility
Dependence
Dynamic random effects
Posterior ratemaking
Time series

Access to Document

10.1016/j.insmatheco.2021.10.005

Cite this

@article{f5f0d85263f64b84b9f04c717b7d05ba,

title = "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 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.",

keywords = "Auto insurance, Credibility, Dependence, Dynamic random effects, Posterior ratemaking, Time series",

author = "{Youn Ahn}, Jae and Himchan Jeong and Yang Lu",

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: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = nov,

doi = "10.1016/j.insmatheco.2021.10.005",

language = "English",

volume = "101",

pages = "626--638",

journal = "Insurance: Mathematics and Economics",

issn = "0167-6687",

publisher = "Elsevier B.V.",

}

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 -

On the ordering of credibility factors

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this