Case Study: French Motor Third-Party Liability Claims

Noll, Alexander; Salzmann, Robert; Wüthrich, Mario V.

doi:10.2139/ssrn.3164764

Cited by 36 publications

(53 citation statements)

References 22 publications

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“…This data set has been recently explored with different statistical and machine learning techniques in Noll et al (2018). We refer the reader to this case study for a broad description of the data and models' implementation details.…”

Section: Frequencymentioning

confidence: 99%

“…Noll et al (2018) compare different models based on in-and out-of-sample errors. The exact definitions for the in-sample and out-ofsample errors are given by formulas (2.2) and (2.3) in Noll et al (2018). In this section we compare some of these models (also built upon a Poisson deviance loss function) using the goodness-of-lift metrics introduced in this paper.…”

Section: Frequencymentioning

confidence: 99%

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Model selection based on Lorenz and concentration curves, Gini indices and convex order

Denuit

Sznajder

Trufin

2019

Insurance: Mathematics and Economics

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In order to determine an appropriate amount of premium, statistical goodness-of-fit criteria must be supplemented with actuarial ones when assessing performance of a given candidate pure premium. In this paper, concentration curves and Lorenz curves are shown to provide actuaries with effective tools to evaluate whether a premium is appropriate or to compare two competing alternatives. The idea is to compare the premium income for sub-portfolios gathering low risks (identified as low by means of the premiums under consideration) to the true one, or equivalently, to the actual losses. Numerical illustrations performed on hypothetical data and real ones demonstrate the usefulness of the proposed approach.

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Section: Frequencymentioning

confidence: 99%

Section: Frequencymentioning

confidence: 99%

Model selection based on Lorenz and concentration curves, Gini indices and convex order

Denuit

Sznajder

Trufin

2019

Insurance: Mathematics and Economics

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show abstract

“…preprocess as in Noll, Salzmann, and Wuthrich [32], except deleting records that have positive claim frequency but have no claim severity and also except using different partitions on variables "VehAge" and "DrivAge". After the data preprocess, the dataset contains 668897 records.…”

Section: Plos Onementioning

confidence: 99%

“…We consider a French motor third-party liability dataset, where the data "freMTPL2freq" and "freMTPL2sev" are in the R package "CASdatasets". Noll, Salzmann, and Wuthrich [32] use the data "freMTPL2freq" to compare the GLM, regression tree, gradient boosting Poisson model and neural network in predicting the claim frequency. We make the same data…”

Section: Datamentioning

confidence: 99%

“…Kriegler and Berk [31] introduce the boosting quantile regression model. In actuarial literature, Noll, Salzmann, and Wuthrich [32] show that the boosting Poisson regression model performs better than the GLM model in predicting the claim frequency. Yang, Qian, and Zou [33] develop a gradient boosting Tweedie compound Poisson model, where they use a profile likelihood approach to estimate the index and dispersion parameters.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic gradient boosting frequency-severity model of insurance claims

Su¹,

Bai²

2020

PLoS ONE

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The standard GLM and GAM frequency-severity models assume independence between the claim frequency and severity. To overcome restrictions of linear or additive forms and to relax the independence assumption, we develop a data-driven dependent frequency-severity model, where we combine a stochastic gradient boosting algorithm and a profile likelihood approach to estimate parameters for both of the claim frequency and average claim severity distributions, and where we introduce the dependence between the claim frequency and severity by treating the claim frequency as a predictor in the regression model for the average claim severity. The model can flexibly capture the nonlinear relation between the claim frequency (severity) and predictors and complex interactions among predictors and can fully capture the nonlinear dependence between the claim frequency and severity. A simulation study shows excellent prediction performance of our model. Then, we demonstrate the application of our model with a French auto insurance claim data. The results show that our model is superior to other state-of-the-art models.

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Evaluation and interpretation of driving risks: Automobile claim frequency modeling with telematics data

Gao

Huang

Meng

2022

Statistical Analysis

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With the development of vehicle telematics and data mining technology, usage-based insurance (UBI) has aroused widespread interest from both academia and industry. The extensive driving behavior features make it possible to further understand the risks of insured vehicles, but pose challenges in the identification and interpretation of important ratemaking factors. This study, based on the telematics data of policyholders in China's mainland, analyzes insurance claim frequency of commercial trucks using both Poisson regression and several machine learning models, including regression tree, random forest, gradient boosting tree, XGBoost and neural network. After selecting the best model, we analyze feature importance, feature effects and the contribution of each feature to the prediction from an actuarial perspective. Our empirical study shows that XGBoost greatly outperforms the traditional models and detects some important risk factors, such as the average speed, the average mileage traveled per day, the fraction of night driving, the number of sudden brakes and the fraction of left/right turns at intersections. These features usually have a nonlinear effect on driving risk, and there are complex interactions between features. To further distinguish high−/low-risk drivers, we run supervised clustering for risk segmentation according to drivers' driving habits. In summary, this study not only provide a more accurate prediction of driving risk, but also greatly satisfy the interpretability requirements of insurance regulators and risk management.

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Case Study: French Motor Third-Party Liability Claims

Cited by 36 publications

References 22 publications

Model selection based on Lorenz and concentration curves, Gini indices and convex order

Model selection based on Lorenz and concentration curves, Gini indices and convex order

Stochastic gradient boosting frequency-severity model of insurance claims

Evaluation and interpretation of driving risks: Automobile claim frequency modeling with telematics data

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