City Research Online

A multi-task network approach for calculating discrimination-free insurance prices

Lindholm, M., Richman, R., Tsanakas, A. ORCID: 0000-0003-4552-5532 & Wüthrich, M. V. (2023). A multi-task network approach for calculating discrimination-free insurance prices. European Actuarial Journal, doi: 10.1007/s13385-023-00367-z


In applications of predictive modeling, such as insurance pricing, indirect or proxy discrimination is an issue of major concern. Namely, there exists the possibility that protected policyholder characteristics are implicitly inferred from non-protected ones by predictive models and are thus having an undesirable (and possibly illegal) impact on prices. A technical solution to this problem relies on building a best-estimate model using all policyholder characteristics (including protected ones) and then averaging out the protected characteristics for calculating individual prices. However, such an approach requires full knowledge of policyholders’ protected characteristics, which may in itself be problematic. Here, we address this issue by using a multi-task neural network architecture for claim predictions, which can be trained using only partial information on protected characteristics and produces prices that are free from proxy discrimination. We demonstrate the proposed method on both synthetic data and a real-world motor claims dataset, in which proxy discrimination can be observed. In both examples we find that the predictive accuracy of the multi-task network is comparable to a conventional feed-forward neural network, when the protected information is available for at least half of the insurance policies. However, the multi-task network has superior performance in the case when the protected information is known for less than half of the insurance policyholders.

Publication Type: Article
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Publisher Keywords: Indirect discrimination, Proxy discrimination, Discrimination-free insurance pricing, Unawareness price, Best-estimate price, Protected information, Discriminatory covariates, Fairness, Incomplete information, Multi-task learning, Multi-output network
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:
[thumbnail of s13385-023-00367-z.pdf]
Text - Published Version
Available under License Creative Commons: Attribution International Public License 4.0.

Download (1MB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login