Extension and application of credibility models in predicting claim frequency
type: Item
instance of: scholarly article
title: Extension and application of credibility models in predicting claim frequency
zbMATH Open document ID: 1427.91246
DOI: 10.1155/2018/6250686
author: Yuan-tao Xie
author: Zheng-xiao Li
author: Rahul A. Parsa
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: In nonlife actuarial science, credibility models are one of the main methods of experience ratemaking. Bühlmann-Straub credibility model can be expressed as a special case of linear mixed models (LMMs) with the underlying assumption of normality. In this paper, we extend the assumption of Bühlmann-Straub model to include Poisson and negative binomial distributions as they are more appropriate for describing the distribution of a number of claims. By using the framework of generalized linear mixed models (GLMMs), we obtain the generalized credibility premiums that contain as particular cases another credibility premium in the literature. Compared to generalized linear mixed models, our extended credibility models also have an advantage in that the credibility factor falls into the range from 0 to 1. The performance of our models in comparison with an existing model in the literature is also evaluated through numerical studies, which shows that our approach produces premium estimates close to the optima. In addition, our proposed model can also be applied to the most commonly used ratemaking approach, namely, the net, the optimal Bonus-Malus system.
Mathematics Subject Classification ID: 91G05
Mathematics Subject Classification ID: 62P05
zbMATH DE Number: 7019265
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6250686
OpenAlex ID: W2790981143
cites work: Loss models. From data to decisions
cites work: Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance
cites work: OPTIMAL BONUS-MALUS SYSTEMS USING FINITE MIXTURE MODELS
cites work: A longitudinal data analysis interpretation of credibility models
cites work: A generalization of the credibility theory obtained by using the weighted balanced loss function
cites work: Some Bayesian credibility premiums obtained by using posterior regret \(\Gamma\)-minimax methodology
cites work: A Flexible Bayesian Nonparametric Model for Predicting Future Insurance Claims
cites work: Credibility Estimation of Distribution Functions with Applications to Experience Rating in General Insurance
cites work: A new approach to the credibility formula
cites work: Actuarial statistics with generalized linear mixed models
cites work: A course in credibility theory and its applications
cites work: Actuarial Modelling of Claim Counts
description: scientific article; zbMATH DE number 7019265