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What is fair? Proxy discrimination vs. demographic disparities in insurance pricing

Lindholm, M., Richman, R., Tsanakas, A. ORCID: 0000-0003-4552-5532 & Wüthrich, M. V. (2024). What is fair? Proxy discrimination vs. demographic disparities in insurance pricing. Scandinavian Actuarial Journal,


Discrimination and fairness are major concerns in algorithmic models. This is particularly true in insurance, where protected policyholder attributes are not allowed to be used for insurance pricing. Simply disregarding protected policyholder attributes is not an appropriate solution, as this still allows for the possibility of inferring protected attributes from non-protected covariates, leading to the phenomenon of proxy discrimination. Though proxy discrimination is qualitatively different from the group fairness concepts discussed in the machine learning and actuarial literatures, group fairness criteria have been proposed to control the impact of protected attributes on the calculation of insurance prices. The purpose of this paper is to discuss the relationship between, on the one hand, direct and proxy discrimination in insurance and, on the other, the most popular group fairness axioms. We provide a technical definition of proxy discrimination and derive incompatibility results, showing that avoiding proxy discrimination does not imply satisfying group fairness and vice versa. This shows that the two concepts are materially different. Furthermore, we discuss input data pre-processing and model post-processing methods that achieve group fairness in the sense of demographic parity, using as a main tool the theory of optimal transport. As these methods induce transformations that explicitly depend on policyholders’ protected attributes, it becomes ambiguous whether they can be said to avoid direct and proxy discrimination.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article to be published by Taylor & Francis in Scandinavian Actuarial Journal, to be available at:
Publisher Keywords: Discrimination, indirect discrimination, proxy discrimination, fairness, protected attributes, discrimination-free, unawareness, group fairness, demographic parity, statistical parity, independence axiom, equalized odds, separation axiom, predictive parity, sufficiency axiom, input pre-processing, output post-processing, optimal transport, Wasserstein distance.
Subjects: H Social Sciences > HF Commerce
H Social Sciences > HG Finance
H Social Sciences > HN Social history and conditions. Social problems. Social reform
Departments: Bayes Business School
Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:
[thumbnail of What_is_Fair_Accepted.pdf] Text - Accepted Version
This document is not freely accessible due to copyright restrictions.

Supplementary Materials:


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