Bayesian premium of a credibility model based on a heterogeneous SETINAR(2, 1) process

In this paper, we propose a new credibility model based on heterogeneous integer-valued self-exciting threshold autoregressive time series, in which the SETINAR(2, 1) process is used to fit the claim numbers of policyholders for consecutive periods, and the unobservable heterogeneity is assumed to f...

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Published inAIMS mathematics Vol. 8; no. 12; pp. 28710 - 28727
Main Authors Zhang, Shuo, Cheng, Jianhua
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
automobile insurance
bayesian premium
credibility model
setinar(2， 1) process
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ISSN2473-6988
2473-6988
DOI10.3934/math.20231469

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Abstract In this paper, we propose a new credibility model based on heterogeneous integer-valued self-exciting threshold autoregressive time series, in which the SETINAR(2, 1) process is used to fit the claim numbers of policyholders for consecutive periods, and the unobservable heterogeneity is assumed to follow Gamma distribution. We obtain the Bayesian pricing formula for the proposed model and present some numerical examples to illustrate how the claim history affects the future premiums. We also apply the proposed model to a real panel dataset from the Wisconsin Local Government Property Insurance Fund. By comparing with some existing models, we find that our model can exploit the past information more efficiently and has better predictive performance.
AbstractList In this paper, we propose a new credibility model based on heterogeneous integer-valued self-exciting threshold autoregressive time series, in which the SETINAR(2, 1) process is used to fit the claim numbers of policyholders for consecutive periods, and the unobservable heterogeneity is assumed to follow Gamma distribution. We obtain the Bayesian pricing formula for the proposed model and present some numerical examples to illustrate how the claim history affects the future premiums. We also apply the proposed model to a real panel dataset from the Wisconsin Local Government Property Insurance Fund. By comparing with some existing models, we find that our model can exploit the past information more efficiently and has better predictive performance.
Author Cheng, Jianhua
Zhang, Shuo
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Cites_doi 10.1111/j.1467-9892.1987.tb00438.x
10.1080/03461238.2012.670611
10.3390/risks4010004
10.1016/j.insmatheco.2018.06.003
10.3390/math9050505
10.1080/03610926.2011.556292
10.1007/3-540-29273-X
10.1046/j.0022-4367.2003.00066.x
10.1080/03461238.2019.1655477
10.2143/AST.31.2.1009
10.1016/j.insmatheco.2016.01.003
10.1515/demo-2018-0022
10.1007/s13385-023-00351-7
10.2139/ssrn.4170555
10.1016/j.insmatheco.2003.11.005
10.1002/9780470517420
10.1017/S0269964821000188
10.3390/risks2010049
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SubjectTerms automobile insurance
bayesian premium
credibility model
setinar(2， 1) process
Title Bayesian premium of a credibility model based on a heterogeneous SETINAR(2, 1) process
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