Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models

David, Mihaela; Jemna, Dănuţ-Vasile

doi:10.1515/aicue-2015-0011

Cited by 15 publications

(8 citation statements)

References 38 publications

(54 reference statements)

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“…Ver Hoef and Boveng (2007) illustrated the restriction of Poisson in modeling count data in ecology and suggested relative merits in quasi-Poisson regression and negative binomial regression over Poisson. When tests were conducted on the motor claim insurance frequency data, the negative binomial model was found to correct the overdispersion and presented a better fit for the data (David and Jemna 2015). In Naya et al (2008), the authors compared the performance of Poisson and ZIP models under four simulation scenarios to analyze field data and established that the ZIP models gave better estimates than the Poisson models.…”

Section: Literature Reviewmentioning

confidence: 99%

Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing

Lee¹

2020

Risks

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This study proposes an efficacious approach to analyze the over-dispersed insurance frequency data as it is imperative for the insurers to have decisive informative insights for precisely underwriting and pricing insurance products, retaining existing customer base and gaining an edge in the highly competitive retail insurance market. The delta boosting implementation of the negative binomial regression, both by one-parameter estimation and a novel two-parameter estimation, was tested on the empirical data. Accurate parameter estimation of the negative binomial regression is complicated with considerations of incomplete insurance exposures, negative convexity, and co-linearity. The issues mainly originate from the unique nature of insurance operations and the adoption of distribution outside the exponential family. We studied how the issues could significantly impact the quality of estimation. In addition to a novel approach to simultaneously estimate two parameters in regression through boosting, we further enrich the study by proposing an alteration of the base algorithm to address the problems. The algorithm was able to withstand the competition against popular regression methodologies in a real-life dataset. Common diagnostics were applied to compare the performance of the relevant candidates, leading to our conclusion to move from light-tail Poisson to negative binomial for over-dispersed data, from generalized linear model (GLM) to boosting for non-linear and interaction patterns, from one-parameter to two-parameter estimation to reflect more closely the reality.

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Section: Literature Reviewmentioning

confidence: 99%

Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing

Lee¹

2020

Risks

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“…Pemodelan frekuensi klaim yang telah dilakukan dalam kasus asuransi kendaraan bermotor seperti pemodelan frekuensi klaim menggunakan distribusi Gomez-Deniz Et. Al [5], dan pemodelan frekuensi klaim yang dilakukan menggunakan generalized linier model dengan asumsi data frekuensi klaim berdistribusi binomial negatif [3]. Pemodelan frekuensi klaim lain yang telah dilakukan yaitu pemodelan frekuensi klaim menggunakan generalized liniear model dengan asumsi data frekuensi klaim berdistribusi Hurdle-Poisson [2] dan pemodelan frekuensi klaim menggunakan model binomial negatif dan geometrik [10].…”

Section: Pendahuluanunclassified

Modeling Claim Frequency in Indonesia Auto Insurance Using Generalized Poisson-Lindley Linear Model

Karim

Mutaqin

2020

JMSK

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This paper will discuss the modeling of claim frequency from Indonesian auto insurance using the generalized Poisson-Lindley linear model. This modeling method assumes that the data of claim frequency are from populations that follow generalized Poisson-Lindley distribution. Generalized Poisson-Lindley linear model is an alternative to modeling count data that contains overdispersion. The parameters in the generalized Poisson-Lindley linear model can be estimated using the maximum likelihood estimation method through Newton Raphson's iteration numerical method. The data are the secondary data took from XYZ Company for the 2013 policy which is overdispersed. The data contains policyholder partial loss claims for comprehensive motor vehicle insurance products. From the research conducted it was concluded that the data is suitable to be modeled with generalized Poisson-Lindley linear models and produce better models than ordinary Poisson linear modeling because of produced the smaller AIC value. Of the 3 predictor variables that are modeled on the frequency of claims, 2 variables influenced they are the use variable and vehicle brand variable.

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“…The coefficients of auto burden index and driving areas did not pass the significance test in the two distributions, so that they require to be further analyzed. David and Jemna (2015) fitted the claim frequency with the Poisson distribution and the Negative Binomial distribution respectively, they pointed out that the Negative Binomial distribution fitted claim frequency better than the Poisson distribution. According to the fitting results of the Poisson and negative binomial distributions of the claim frequency, the p-value of the estimated parameters in Poisson distribution is obviously smaller than that of the negative binomial distribution, indicating that the fitting result of Poisson distribution is relatively better.…”

Section: Loss Distribution Of Claim Frequencymentioning

confidence: 99%

A Logistic Regression Based Auto Insurance Rate-Making Model Designed for the Insurance Rate Reform

Duan

Chang

Wang

et al. 2018

IJFS

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Abstract:Using a generalized linear model to determine the claim frequency of auto insurance is a key ingredient in non-life insurance research. Among auto insurance rate-making models, there are very few considering auto types. Therefore, in this paper we are proposing a model that takes auto types into account by making an innovative use of the auto burden index. Based on this model and data from a Chinese insurance company, we built a clustering model that classifies auto insurance rates into three risk levels. The claim frequency and the claim costs are fitted to select a better loss distribution. Then the Logistic Regression model is employed to fit the claim frequency, with the auto burden index considered. Three key findings can be concluded from our study. First, more than 80% of the autos with an auto burden index of 20 or higher belong to the highest risk level. Secondly, the claim frequency is better fitted using the Poisson distribution, however the claim cost is better fitted using the Gamma distribution. Lastly, based on the AIC criterion, the claim frequency is more adequately represented by models that consider the auto burden index than those do not. It is believed that insurance policy recommendations that are based on Generalized linear models (GLM) can benefit from our findings.

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Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models

Abstract: Abstract

Cited by 15 publications

References 38 publications

Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing

Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing

Modeling Claim Frequency in Indonesia Auto Insurance Using Generalized Poisson-Lindley Linear Model

A Logistic Regression Based Auto Insurance Rate-Making Model Designed for the Insurance Rate Reform

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