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

arXiv: https://arxiv.org/abs/2103.03635 · HTML: https://mlsanity.com/paper/2103.03635/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 24 references that are in the map.
- First posted on arXiv 5 Mar 2021.

## Builds on (most cited first, 2 of 2)

- [Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings](https://mlsanity.com/paper/1503.08195/) (2015)
- [Generic Conditions for Forecast Dominance](https://mlsanity.com/paper/1805.09902/) (2018)

## Built on by (most cited first, 18 of 18)

- [Isotonic Recalibration under a Low Signal-to-Noise Ratio](https://mlsanity.com/paper/2301.02692/) (2023)
- [A Fair Pricing Model via Adversarial Learning](https://mlsanity.com/paper/2202.12008/) (2022)
- [Neural networks for insurance pricing with frequency and severity data: a benchmark study from data preprocessing to technical tariff](https://mlsanity.com/paper/2310.12671/) (2023)
- [Model selection with Gini indices under auto-calibration](https://mlsanity.com/paper/2207.14372/) (2022)
- [Enhancing Actuarial Non-Life Pricing Models via Transformers](https://mlsanity.com/paper/2311.07597/) (2023)
- [Bayesian CART models for insurance claims frequency](https://mlsanity.com/paper/2303.01923/) (2023)
- [Insights From Insurance for Fair Machine Learning](https://mlsanity.com/paper/2306.14624/) (2023)
- [Churn modeling of life insurance policies via statistical and machine learning methods -- Analysis of important features](https://mlsanity.com/paper/2202.09182/) (2022)
- [Bayesian CART models for aggregate claim modeling](https://mlsanity.com/paper/2409.01908/) (2024)
- [From Point to probabilistic gradient boosting for claim frequency and severity prediction](https://mlsanity.com/paper/2412.14916/) (2024)
- [Calibration Bands for Mean Estimates within the Exponential Dispersion Family](https://mlsanity.com/paper/2503.18896/) (2025)
- [On the use of case estimate and transactional payment data in neural networks for individual loss reserving](https://mlsanity.com/paper/2601.05274/) (2025)
- [Reinforcement Learning for Micro-Level Claims Reserving](https://mlsanity.com/paper/2601.07637/) (2026)
- [Assessing model calibration with boosting trees](https://mlsanity.com/paper/2606.08084/) (2026)
- [Telematics Combined Actuarial Neural Networks for Cross-Sectional and Longitudinal Claim Count Data](https://mlsanity.com/paper/2308.01729/) (2023)
- [Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurance](https://mlsanity.com/paper/2503.21321/) (2025)
- [Tweedie Regression for Video Recommendation System](https://mlsanity.com/paper/2505.06445/) (2025)
- [A Longitudinal Attribute-Conditioned Neural Network for Modeling Health-State Transition Probabilities in Temporally Irregular Data: The LANTERN Framework](https://mlsanity.com/paper/2606.13880/) (2026)

## Abstract (arXiv)

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).