A Multi-Task Network Approach for Calculating Discrimination-Free Insurance Prices

33 Pages Posted: 19 Jul 2022 Last revised: 2 Nov 2022

See all articles by Mathias Lindholm

Mathias Lindholm

Stockholm University

Ronald Richman

Old Mutual Insure; University of the Witwatersrand

Andreas Tsanakas

Bayes Business School (formerly Cass), City, University of London

Mario V. Wuthrich

RiskLab, ETH Zurich

Date Written: November 2, 2022


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 approaches require 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 it 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 cases we find that the predictive accuracy of the multi-task network is comparable to a conventional feed-forward neural network, when full information is available. Moreover, the multi-task network has clearly superior performance in the case of partially missing policyholder information.

Keywords: indirect discrimination, proxy discrimination, discrimination-free insurance pricing, unawareness price, best-estimate price, protected information, discriminatory covariates, fairness, incomplete information, multi-task learning, multioutput network

JEL Classification: G22, C45, C10, C13, C20

Suggested Citation

Lindholm, Mathias and Richman, Ronald and Tsanakas, Andreas and Wuthrich, Mario V., A Multi-Task Network Approach for Calculating Discrimination-Free Insurance Prices (November 2, 2022). Available at SSRN: https://ssrn.com/abstract=4155585 or http://dx.doi.org/10.2139/ssrn.4155585

Mathias Lindholm

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91

Ronald Richman

Old Mutual Insure ( email )

Wanooka Place
St Andrews Road
Johannesburg, 2192
South Africa

University of the Witwatersrand ( email )

1 Jan Smuts Avenue
Johannesburg, GA Gauteng 2000
South Africa

Andreas Tsanakas

Bayes Business School (formerly Cass), City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Mario V. Wuthrich (Contact Author)

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092

Do you have negative results from your research you’d like to share?

Paper statistics

Abstract Views
PlumX Metrics