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

Shuo Zhang; Jianhua Cheng; Shuo Zhang; Jianhua Cheng

doi:10.3934/math.20231469

AIMS Mathematics

2023, Volume 8, Issue 12: 28710-28727. doi: 10.3934/math.20231469

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Research article

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

Shuo Zhang ¹,
Jianhua Cheng ^{2
,
,}

1.
School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
2.
School of Mathematics, Jilin University, Changchun 130012, China

Received: 29 July 2023 Revised: 12 October 2023 Accepted: 17 October 2023 Published: 23 October 2023
MSC : 62P05, 91B30, 97M30

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.
- automobile insurance,
- credibility model,
- Bayesian premium,
- SETINAR(2, 1) process
Citation: Shuo Zhang, Jianhua Cheng. Bayesian premium of a credibility model based on a heterogeneous SETINAR(2, 1) process[J]. AIMS Mathematics, 2023, 8(12): 28710-28727. doi: 10.3934/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.

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