Multivariate Zero-Inflated INAR(1) Model with an Application in Automobile Insurance

Pengcheng Zhang, Zezhun Chen, George Tzougas, Enrique Calderín–Ojeda, Angelos Dassios and Xueyuan Wu

North American Actuarial Journal, 2025, vol. 29, issue 2, 310-328

Abstract: The objective of this article is to propose a comprehensive solution for analyzing multidimensional non-life claim count data that exhibits time and cross-dependence, as well as zero inflation. To achieve this, we introduce a multivariate INAR(1) model, with the innovation term characterized by either a multivariate zero-inflated Poisson distribution or a multivariate zero-inflated hurdle Poisson distribution. Additionally, our modeling framework accounts for the impact of individual and coverage-specific covariates on the mean parameters of each model, thereby facilitating the computation of customized insurance premiums based on varying risk profiles. To estimate the model parameters, we employ a novel expectation-maximization (EM) algorithm. Our model demonstrates satisfactory performance in the analysis of European motor third-party liability claim count data.

Date: 2025
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DOI: 10.1080/10920277.2024.2381726

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