TY - JOUR
T1 - A multi-year microlevel collective risk model
AU - Oh, Rosy
AU - Jeong, Himchan
AU - Ahn, Jae Youn
AU - Valdez, Emiliano A.
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. Rosy Oh was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2020R1I1A1A01067376 ). Himchan Jeong was supported by James C. Hickman Doctoral Stipend funded by the Society of Actuaries (SOA). Emiliano A. Valdez was supported by CAE Research Grant on Applying Data Mining Techniques in Actuarial Science funded by the Society of Actuaries (SOA). Jae Youn Ahn was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government ( 2020R1F1A1A01061202 ).
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/9
Y1 - 2021/9
N2 - For a typical insurance portfolio, the claims process for a short period, typically one year, is characterized by observing frequency of claims together with the associated claims severities. The collective risk model describes this portfolio as a random sum of the aggregation of the claim amounts. In the classical framework, for simplicity, the claim frequency and claim severities are assumed to be mutually independent. However, there is a growing interest in relaxing this independence assumption which is more realistic and useful for the practical insurance ratemaking. While the common thread has been capturing the dependence between frequency and aggregate severity within a single period, the work of Oh et al. (2021) provides an interesting extension to the addition of capturing dependence among individual severities. In this paper, we extend these works within a framework where we have a portfolio of microlevel frequencies and severities for multiple years. This allows us to develop a factor copula model framework that captures various types of dependence between claim frequencies and claim severities over multiple years. It is therefore a clear extension of earlier works on one-year dependent frequency-severity models and on random effects model for capturing serial dependence of claims. We focus on the results using a family of elliptical copulas to model the dependence. The paper further describes how to calibrate the proposed model using illustrative claims data arising from a Singapore insurance company. The estimated results provide strong evidences of all forms of dependencies captured by our model.
AB - For a typical insurance portfolio, the claims process for a short period, typically one year, is characterized by observing frequency of claims together with the associated claims severities. The collective risk model describes this portfolio as a random sum of the aggregation of the claim amounts. In the classical framework, for simplicity, the claim frequency and claim severities are assumed to be mutually independent. However, there is a growing interest in relaxing this independence assumption which is more realistic and useful for the practical insurance ratemaking. While the common thread has been capturing the dependence between frequency and aggregate severity within a single period, the work of Oh et al. (2021) provides an interesting extension to the addition of capturing dependence among individual severities. In this paper, we extend these works within a framework where we have a portfolio of microlevel frequencies and severities for multiple years. This allows us to develop a factor copula model framework that captures various types of dependence between claim frequencies and claim severities over multiple years. It is therefore a clear extension of earlier works on one-year dependent frequency-severity models and on random effects model for capturing serial dependence of claims. We focus on the results using a family of elliptical copulas to model the dependence. The paper further describes how to calibrate the proposed model using illustrative claims data arising from a Singapore insurance company. The estimated results provide strong evidences of all forms of dependencies captured by our model.
KW - Collective risk model
KW - Copula model
KW - Predictivce analysis
KW - Random effect model
UR - http://www.scopus.com/inward/record.url?scp=85110225555&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2021.06.006
DO - 10.1016/j.insmatheco.2021.06.006
M3 - Article
AN - SCOPUS:85110225555
SN - 0167-6687
VL - 100
SP - 309
EP - 328
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -