Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning

TL;DR

This paper investigates the bias issues in insurance pricing models trained with Tweedie deviance, introduces autocalibration as a bias correction method, and demonstrates its theoretical benefits for local balance in premium calculations.

Contribution

It proposes a novel autocalibration method that corrects bias in machine learning models trained with Tweedie deviance, ensuring local balance in insurance premium estimation.

Findings

Autocalibration effectively corrects bias in Tweedie-based models.

The method guarantees local balance in premium calculations.

Convex order provides a new framework for model comparison.

Abstract

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).