Bayesian Cart Models for Insurance Claims Frequency

42 Pages Posted: 6 Mar 2023

See all articles by Yaojun Zhang

Yaojun Zhang

University of Leeds

Lanpeng Ji

University of Leeds

Georgios Aivaliotis

University of Leeds - School of Mathematics and Statistics

Charles Taylor

University of Leeds

Abstract

Accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, the classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easily interpretable. In this paper, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling.  Additionally to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration.  We also introduce the deviance information criterion (DIC) for the tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Some simulations and real insurance data will be discussed to illustrate the applicability of these models.

Keywords: Insurance pricing, claims frequency, Bayesian CART, MCMC, DIC

Suggested Citation

Zhang, Yaojun and Ji, Lanpeng and Aivaliotis, Georgios and Taylor, Charles, Bayesian Cart Models for Insurance Claims Frequency. Available at SSRN: https://ssrn.com/abstract=4379998 or http://dx.doi.org/10.2139/ssrn.4379998

Yaojun Zhang

University of Leeds ( email )

Leeds, LS2 9JT
United Kingdom

Lanpeng Ji (Contact Author)

University of Leeds ( email )

Leeds, LS2 9JT
United Kingdom

Georgios Aivaliotis

University of Leeds - School of Mathematics and Statistics ( email )

Leeds LS2 9JT
United Kingdom

Charles Taylor

University of Leeds ( email )

Leeds, LS2 9JT
United Kingdom

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