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Enhanced Gradient Boosting for Zero-Inflated Insurance Claims and Comparative Analysis of CatBoost, XGBoost, and LightGBM

Banghee So

TL;DR

This paper investigates the use of boosting algorithms to process insurance claim data, including zero-inflated telematics data, to construct claim frequency models and proposes a new zero-inflated Poisson boosted tree model, which outperforms others depending on the characteristics of the data.

Abstract

The property and casualty (P&C) insurance industry faces challenges in developing claim predictive models due to the highly right-skewed distribution of positive claims with excess zeros. To address this, actuarial science researchers have employed "zero-inflated" models that combine a traditional count model and a binary model. This paper investigates the use of boosting algorithms to process insurance claim data, including zero-inflated telematics data, to construct claim frequency models. Three popular gradient boosting libraries - XGBoost, LightGBM, and CatBoost - are evaluated and compared to determine the most suitable library for training insurance claim data and fitting actuarial frequency models. Through a comprehensive analysis of two distinct datasets, it is determined that CatBoost is the best for developing auto claim frequency models based on predictive performance. Furthermore, we propose a new zero-inflated Poisson boosted tree model, with variation in the assumption about the relationship between inflation probability $p$ and distribution mean $μ$, and find that it outperforms others depending on data characteristics. This model enables us to take advantage of particular CatBoost tools, which makes it easier and more convenient to investigate the effects and interactions of various risk features on the frequency model when using telematics data.

Enhanced Gradient Boosting for Zero-Inflated Insurance Claims and Comparative Analysis of CatBoost, XGBoost, and LightGBM

TL;DR

This paper investigates the use of boosting algorithms to process insurance claim data, including zero-inflated telematics data, to construct claim frequency models and proposes a new zero-inflated Poisson boosted tree model, which outperforms others depending on the characteristics of the data.

Abstract

The property and casualty (P&C) insurance industry faces challenges in developing claim predictive models due to the highly right-skewed distribution of positive claims with excess zeros. To address this, actuarial science researchers have employed "zero-inflated" models that combine a traditional count model and a binary model. This paper investigates the use of boosting algorithms to process insurance claim data, including zero-inflated telematics data, to construct claim frequency models. Three popular gradient boosting libraries - XGBoost, LightGBM, and CatBoost - are evaluated and compared to determine the most suitable library for training insurance claim data and fitting actuarial frequency models. Through a comprehensive analysis of two distinct datasets, it is determined that CatBoost is the best for developing auto claim frequency models based on predictive performance. Furthermore, we propose a new zero-inflated Poisson boosted tree model, with variation in the assumption about the relationship between inflation probability and distribution mean , and find that it outperforms others depending on data characteristics. This model enables us to take advantage of particular CatBoost tools, which makes it easier and more convenient to investigate the effects and interactions of various risk features on the frequency model when using telematics data.
Paper Structure (15 sections, 34 equations, 6 figures, 6 tables, 2 algorithms)

This paper contains 15 sections, 34 equations, 6 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Gradient Boosting Machine
  3. Generic algorithm
  4. Comparison between XGBoost, LightGBM and CatBoost
  5. Zero-Inflated Poisson Boosted Tree
  6. $p$ is a function of $\mu$
  7. $p$ and $\mu$ are unrelated
  8. Experimental results
  9. Performance evaluation
  10. Deviance / Pseudo R-squared
  11. Vuong test
  12. Randomized Quantile Residuals
  13. French Motor Third-Party Liability
  14. Synthetic telematics data
  15. Concluding remarks

Figures (6)

  • Figure 2: Q-Q Plots of Randomized Quantile Residuals: Five Models for French Motor Third-Party Liability Data - CatBoost ZIPB1 (upper left), CatBoost ZIPB2 (upper middle), CatBoost PB (upper right), ZIPG (bottom left), PG (bottom right)
  • Figure 3: Q-Q Plots of Randomized Quantile Residuals: Five Models for Synthetic Telematics Data - CatBoost ZIPB1 (upper left), CatBoost ZIPB2 (upper middle), CatBoost PB (upper right), ZIPG (bottom left), PG (bottom right)
  • Figure 4: Top 10 Feature Importance in CatBoost ZIPB1
  • Figure 5: Top 10 Features Interation Strength in CatBoost ZIPB1
  • Figure 6: SHAP Values of Top 10 Features in CatBoost ZIPB1
  • ...and 1 more figures