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

37 Pages Posted: 14 May 2023 Last revised: 4 Feb 2024

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: February 1, 2024

Abstract

Indirect 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 the protected attributes from non-protected covariates. This inference leads to so-called proxy or indirect discrimination. Though proxy discrimination is qualitatively different from the group fairness concepts in the machine learning literature, these group fairness concepts 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 differences between direct and indirect discrimination in insurance and the most popular group fairness axioms. In particular, we show that one does not imply the other, as these concepts are materially different. Furthermore, we discuss input data pre-processing methods and model post-processing methods that achieve both discrimination-free insurance prices and demographic parity group fairness. The main tool of these methods is the theory of optimal transport.

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-process

JEL Classification: G22, G21

Suggested Citation

Lindholm, Mathias and Richman, Ronald and Tsanakas, Andreas and Wuthrich, Mario V., What is fair? Proxy discrimination vs. demographic disparities in insurance pricing (February 1, 2024). Available at SSRN: https://ssrn.com/abstract=4436409 or http://dx.doi.org/10.2139/ssrn.4436409

Mathias Lindholm

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Ronald Richman

Old Mutual Insure ( email )

Wanooka Place
St Andrews Road
Johannesburg, 2192
South Africa

University of the Witwatersrand ( email )

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
Switzerland

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