Bayesian Multivariate Mixed Poisson Models with Copula-Based Mixture

Pengcheng Zhang, Enrique Calderín-Ojeda, Shuanming Li and Xueyuan Wu

North American Actuarial Journal, 2023, vol. 27, issue 3, 560-578

Abstract: It is common practice to use multivariate count modeling in actuarial literature when dealing with claim counts from insurance policies with multiple covers. One possible way to construct such a model is to implement copula directly on discrete margins. However, likelihood inference under this construction involves the computation of multidimensional rectangle probabilities, which could be computationally expensive, especially in the elliptical copula case. Another potential approach is based on the multivariate mixed Poisson model. The crucial work under this method is to find an appropriate multivariate continuous distribution for mixing parameters. By virtue of the copula, this issue could be easily addressed. Under such a framework, the Markov chain Monte Carlo (MCMC) method is a feasible strategy for inference. The usefulness of our model is then illustrated through a real-life example. The empirical analysis demonstrates the superiority of adopting a copula-based mixture over other types of mixtures. Finally, we demonstrate how those fitted models can be applied to the insurance ratemaking problem in a Bayesian context.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10920277.2022.2112233 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:uaajxx:v:27:y:2023:i:3:p:560-578

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/uaaj20

DOI: 10.1080/10920277.2022.2112233

Access Statistics for this article

North American Actuarial Journal is currently edited by Kathryn Baker

More articles in North American Actuarial Journal from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().