Our paper, “A Scalable toolbox for exposing indirect discrimination in insurance rates”, with Olivier and Marie-Pier Côté, is finally out. It is published as a CAS (Casualty Actuarial Society) Working Papers.
According to actuarial standards of practice, insurance pricing relies on grouping policyholders by risk to set adequate premiums. Modern predictive models, especially machine learning, excel at detecting statistical associations to differentiate risks, but they can learn spurious or undesired correlations. This raises concerns when socioeconomic or demographic factors may (intentionally or inadvertently) affect the fairness of insurance pricing.
Fairness in insurance is difficult to operationalize due to its ambiguity. Fairness metrics from the machine learning literature lack the segment-specific relevance actuaries require and are expressed in abstract units that obscure real-world consequences. For actuaries to intervene, proxy effects and unfair biases must be quantified in insurance-relevant terms: dollars and people.
In this paper, we focus on fairness in actuarial pricing. We study the situation where insurance rates should be fair with respect to a categorical (or discretized) sensitive variable, such as race or economic status, and the latter is fully observed (despite the possible privacy challenges).
- We argue that actuarial fairness, solidarity, and causality form the three core dimensions of fairness in insurance pricing:
– Actuarial fairness aligns premiums with expected losses, mitigating cross-subsidies,
– Solidarity aligns premiums across protected groups, mitigating disparities,
– Causality ensures models capture only true risk factors, mitigating proxy effects.- We translate these dimensions into a five-point spectrum of premiums:
– The best-estimate premium is the most accurate predictor of losses using all available information, including the sensitive variable,
– The unaware premium is the most accurate predictor of losses using all information except the sensitive variable,
– The aware premium is the most accurate predictor of losses when controlling for the sensitive variable,
– The corrective premium is the most accurate predictor that enforces similar premium distributions across levels of the sensitive variable,
– The hyperaware premium is the most accurate approximation of the corrective premium that does not directly discriminate on the sensitive variable.- We define actuarially relevant local metrics that quantify the potential monetary impact of unfairness at the policyholder level. Proxy vulnerability is the difference between unaware and aware premiums. It locally measures how much the allowed variables pick up the signal of a missing sensitive variable We define post pricing local metrics to evaluate the fairness of any pricing structure relative to the estimated spectrum.
- We partition policyholders to expose the segments in which unfair discrimination is most severe.
- We integrate these components into a fairness assessment framework that partitions the policyholders, pinpoints segments most affected by unfairness, and evaluates
local metrics to diagnose unfairness and guide intervention.- We illustrate our approach with a large case study inspired by industry practice. The analysis relies a real dataset of approximately 768,000 vehicles insured in Québec
(2016–2017), covering at-fault material damage claims. We examine the fairness of a pseudo commercial price with respect to discretized credit score: low (vulnerable group) vs high. This sensitive variable measures the policyholder’s economic precariousness.
– Proxy vulnerability is both material and skewed: while most policyholders may receive a modest rebate, a vulnerable minority of them could face 15–30% overpricing if the regulation only requires that the sensitive variable be omitted,
– Our integrated framework illustrates that fairness in insurance pricing can be assessed efficiently, with minimal analyst effort. The framework provides simultaneous diagnostics from the three fairness dimensions, translates
unfairness into dollar terms at the individual level, and highlights disparities across population segments.- We provide additional information and the complete code illustrated on a comprehensive simulated data example in the online supplementary material.
Designed for routine portfolio monitoring, our toolbox delivers valuable insights whether or not the sensitive attribute is included in pricing, provided it is available for assessment. The toolbox’s scalability, across large datasets and rich covariate sets, makes fairness operationalizable for actuaries: intuitive, practical, and encompassing the three fairness dimensions.
