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.
Machine learning is a way to use computers to help with insurance pricing. People are still figuring out the best ways to train these computer models. Sometimes, the computer predictions are different from what actually happens. This can cause problems when trying to set prices for insurance. One solution is called autocalibration, which tries to fix these problems by adding extra steps to the analysis. It's important to make sure that the computer models are balanced and accurate so that people can get fair prices for their insurance.
Insurance Pricing with Machine Learning Techniques: A Study on Tweedie Deviance and Autocalibration
The use of machine learning techniques, such as boosting and neural networks, has become increasingly popular in the insurance industry for pricing policies. While these methods have proven to be effective, there are still 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.
In this study, researchers 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.
Models Trained to Minimize Deviance Generally Underestimate Total Claims
The research demonstrates 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.
Convex Order Suggested as Natural Tool for Comparing Models
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 help of averaging observed losses to ensure balance at both portfolio and local levels.
Overall, this research provides valuable insight into how machine learning techniques can be used effectively in insurance pricing while avoiding discrepancies between fitted values and observed totals due to early stopping rules or lack of global balance constraints when minimizing Tweedie deviances
Boosting techniques and neural networks are particularly effective machine learning methods for insurance pricing. Often in practice, there are nevertheless endless debates about the choice of the right loss function to be used to train the machine learning model, as well as about the appropriate metric to assess the performances of competing models. Also, the sum of fitted values can depart from the observed totals to a large extent and this often confuses actuarial analysts. The lack of balance inherent to training models by minimizing deviance outside the familiar GLM with canonical link setting has been empirically documented in W\"uthrich (2019, 2020) who attributes it to the early stopping rule in gradient descent methods for model fitting. The present paper aims to further study this phenomenon when learning proceeds by minimizing Tweedie deviance. It is shown that minimizing deviance involves a trade-off between the integral of weighted differences of lower partial moments and the bias measured on a specific scale. Autocalibration is then proposed as a remedy. This new method to correct for bias adds an extra local GLM step to the analysis. Theoretically, it is shown that it implements the autocalibration concept in pure premium calculation and ensures that balance also holds on a local scale, not only at portfolio level as with existing bias-correction techniques. The convex order appears to be the natural tool to compare competing models, putting a new light on the diagnostic graphs and associated metrics proposed by Denuit et al. (2019).
