# A Fair Pricing Model via Adversarial Learning

arXiv: https://arxiv.org/abs/2202.12008 · HTML: https://mlsanity.com/paper/2202.12008/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 74 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 20 of 20)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [Fairness Under Unawareness: Assessing Disparity When Protected Class Is Unobserved](https://mlsanity.com/paper/1811.11154/) (2018)
- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [Achieving Fairness through Adversarial Learning: an Application to Recidivism Prediction](https://mlsanity.com/paper/1807.00199/) (2018)
- [Learning to Pivot with Adversarial Networks](https://mlsanity.com/paper/1611.01046/) (2016)
- [R'enyi Fair Inference](https://mlsanity.com/paper/1906.12005/) (2019)
- [The Randomized Dependence Coefficient](https://mlsanity.com/paper/1304.7717/) (2013)
- [Fairness without the sensitive attribute via Causal Variational Autoencoder](https://mlsanity.com/paper/2109.04999/) (2021)
- [Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning](https://mlsanity.com/paper/2103.03635/) (2021)
- [A survey on measuring indirect discrimination in machine learning](https://mlsanity.com/paper/1511.00148/) (2015)
- [Generic Conditions for Forecast Dominance](https://mlsanity.com/paper/1805.09902/) (2018)
- [Optimized Data Pre-Processing for Discrimination Prevention](https://mlsanity.com/paper/1704.03354/) (2017)
- [Geographic ratemaking with spatial embeddings](https://mlsanity.com/paper/2104.12852/) (2021)

## Built on by (most cited first, 7 of 7)

- [A multi-task network approach for calculating discrimination-free insurance prices](https://mlsanity.com/paper/2207.02799/) (2022)
- [A Discussion of Discrimination and Fairness in Insurance Pricing](https://mlsanity.com/paper/2209.00858/) (2022)
- [Machine Learning with Multitype Protected Attributes: Intersectional Fairness through Regularisation](https://mlsanity.com/paper/2509.08163/) (2025)
- [Measuring and Mitigating Biases in Motor Insurance Pricing](https://mlsanity.com/paper/2311.11900/) (2023)
- [Discrimination-free Insurance Pricing with Privatized Sensitive Attributes](https://mlsanity.com/paper/2504.11775/) (2025)
- [OptiGrad: A Fair and more Efficient Price Elasticity Optimization via a Gradient Based Learning](https://mlsanity.com/paper/2404.10275/) (2024)
- [Marginal Fairness: Fair Decision-Making under Risk Measures](https://mlsanity.com/paper/2505.18895/) (2025)

## Abstract (arXiv)

At the core of insurance business lies classification between risky and non-risky insureds, actuarial fairness meaning that risky insureds should contribute more and pay a higher premium than non-risky or less-risky ones. Actuaries, therefore, use econometric or machine learning techniques to classify, but the distinction between a fair actuarial classification and "discrimination" is subtle. For this reason, there is a growing interest about fairness and discrimination in the actuarial community Lindholm, Richman, Tsanakas, and Wuthrich (2022). Presumably, non-sensitive characteristics can serve as substitutes or proxies for protected attributes. For example, the color and model of a car, combined with the driver's occupation, may lead to an undesirable gender bias in the prediction of car insurance prices. Surprisingly, we will show that debiasing the predictor alone may be insufficient to maintain adequate accuracy (1). Indeed, the traditional pricing model is currently built in a two-stage structure that considers many potentially biased components such as car or geographic risks. We will show that this traditional structure has significant limitations in achieving fairness. For this reason, we have developed a novel pricing model approach. Recently some approaches have Blier-Wong, Cossette, Lamontagne, and Marceau (2021); Wuthrich and Merz (2021) shown the value of autoencoders in pricing. In this paper, we will show that (2) this can be generalized to multiple pricing factors (geographic, car type), (3) it perfectly adapted for a fairness context (since it allows to debias the set of pricing components): We extend this main idea to a general framework in which a single whole pricing model is trained by generating the geographic and car pricing components needed to predict the pure premium while mitigating the unwanted bias according to the desired metric.