Modelling the aggregate loss for insurance claims with dependence

• Published in: Communications in statistics. Theory and methods Vol. 50; no. 9; pp. 2080 - 2095
• Main Authors: Wang, Ning, Qian, Linyi, Zhang, Nan, Liu, Zehui
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.05.2021; Taylor & Francis Ltd
• Subjects: Algorithms; claim amounts; Claim counts; Dependence; generalized linear mixed models; Generalized linear models; Insurance; Insurance claims; Maximum likelihood estimates; MCEM algorithm; Metropolis-Hastings algorithm; Model testing; Parameter estimation; Statistical models
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2019.1659368

In this paper, we propose a new model to relax the impractical independence assumption between the counts and the amounts of insurance claims, which is commonly made in the existing literature for mathematical convenience. When considering the dependence between the claim counts and the claim amounts, we treat the number of claims as an explanatory variable in the model for claim sizes. Besides, generalized linear models (GLMs) are employed to fit the claim counts in a given time period. To describe the claim amounts which are repeatedly measured on a group of subjects over time, we adopt generalized linear mixed models (GLMMs) to incorporate the dependence among the related observations on the same subject. In addition, a Monte Carlo Expectation-Maximization (MCEM) algorithm is proposed by using a Metropolis-Hastings algorithm sampling scheme to obtain the maximum likelihood estimates of the parameters for the linear predictor and variance component. Finally, we conduct a simulation to illustrate the feasibility of our proposed model.