# Modelling the aggregate loss for insurance claims with dependence

Ning Wang, Linyi Qian, Nan Zhang, Zehui Liu

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

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.
Language English 16 Communications in Statistics - Theory and Methods 10.1080/03610926.2019.1659368 E-pub ahead of print - 2 Sep 2019

### Fingerprint

Insurance
Modeling
Count
Metropolis-Hastings Algorithm
Generalized Linear Mixed Model
Variance Components
Monte Carlo Algorithm
Expectation-maximization Algorithm
Generalized Linear Model
Maximum Likelihood Estimate
Predictors
Model
Simulation

### Keywords

• claim amounts
• Claim counts
• dependence
• generalized linear mixed models
• generalized linear models
• MCEM algorithm
• Metropolis-Hastings algorithm

### Cite this

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title = "Modelling the aggregate loss for insurance claims with dependence",
abstract = "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.",
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Modelling the aggregate loss for insurance claims with dependence. / Wang, Ning; Qian, Linyi; Zhang, Nan; Liu, Zehui.

In: Communications in Statistics - Theory and Methods, 02.09.2019.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Modelling the aggregate loss for insurance claims with dependence

AU - Wang, Ning

AU - Qian, Linyi

AU - Zhang, Nan

AU - Liu, Zehui

PY - 2019/9/2

Y1 - 2019/9/2

N2 - 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.

AB - 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.

KW - claim amounts

KW - Claim counts

KW - dependence

KW - generalized linear mixed models

KW - generalized linear models

KW - MCEM algorithm

KW - Metropolis-Hastings algorithm

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DO - 10.1080/03610926.2019.1659368

M3 - Article

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JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

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