# Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning

**Authors:** Michel Denuit, Arthur Charpentier, Julien Trufin  
**arXiv:** [2103.03635](https://arxiv.org/abs/2103.03635)  
**Date:** 2021-03-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2103.03635v1/

## Key points

- Machine learning techniques like boosting and neural networks are effective for insurance pricing
- Ongoing debates exist regarding appropriate loss function and performance metrics for training these models
- Actuarial analysts struggle with the sum of fitted values differing significantly from observed totals
- Training models by minimizing deviance outside of the familiar Generalized Linear Model (GLM) can result in a lack of balance due to early stopping rule in gradient descent methods for model fitting
- Autocalibration is proposed as a remedy to address this issue, which corrects bias by adding an extra local GLM step to the analysis and ensures balance at both portfolio and local levels
- Tree-based boosting models and neural networks trained to minimize deviance generally underestimate total claims significantly, breaking total balance even on the training data set
- Using deviance as an objective function without global balance constraints may lead to dubious candidate premiums because they can deviate significantly from observed losses when totals are not kept
- The study questions the relevance of using deviance as an objective function without global balance constraints for insurance pricing with machine learning techniques
- The convex order is suggested as a natural tool to compare competing models and put new light on diagnostic graphs and associated metrics
- Actuarial risk classification is established with the help of averaging observed losses to ensure balance at both portfolio and local levels.

## Summary

The use of machine learning techniques, such as boosting and neural networks, has proven to be effective for insurance pricing. However, there are ongoing debates regarding the appropriate loss function and performance metrics for training these models. Additionally, actuarial analysts often struggle with the fact that the sum of fitted values can significantly differ from observed totals. Recent empirical studies have shown that training models by minimizing deviance outside of the familiar Generalized Linear Model (GLM) with canonical link setting can result in a lack of balance. This imbalance is attributed to the early stopping rule in gradient descent methods for model fitting. The present study aims to further investigate this phenomenon when learning proceeds by minimizing Tweedie deviance. The paper shows that minimizing deviance involves a trade-off between the integral of weighted differences of lower partial moments and bias measured on a specific scale. To address this issue, autocalibration is proposed as a remedy. This new method corrects bias by adding an extra local GLM step to the analysis and implements the autocalibration concept in pure premium calculation. It ensures that balance holds not only at portfolio level but also on a local scale. Furthermore, it is demonstrated that tree-based boosting models and neural networks trained to minimize deviance generally underestimate total claims significantly, breaking total balance even on the training data set. This indicates that using deviance as an objective function without global balance constraints may lead to dubious candidate premiums because they can deviate significantly from observed losses when totals are not kept. In conclusion, this study questions the relevance of using deviance as an objective function without global balance constraints for insurance pricing with machine learning techniques. The convex order is suggested as a natural tool to compare competing models and put new light on diagnostic graphs and associated metrics proposed by Denuit et al. (2019). Finally, actuarial risk classification is established with the help of averaging observed losses to ensure balance at both portfolio and local levels.