Tag Archives: cote

Recoverability of market-wide fair insurance premiums under selection bias

Our article, Recoverability of market-wide fair insurance premiums under selection bias, with Marie-Pier Côté and Olivier Côté, was published in Insurance: Mathematics & Economics.

Fairness adjustments in insurance pricing are defined relative to a reference population, i.e., to a joint distribution of (X, D, Y) where X are rating factors, D protected attributes, and Y is claim amount. Because an insurer’s portfolio is generally a selected subpopulation, portfolio and population reference distributions typically differ, so portfolio-calibrated and population-calibrated fairness adjustments need not coincide. In what follows, we use selection bias as an umbrella term for any discrepancy between an observed sample and its target population. We call portfolio composition bias the insurance-specific form of selection bias induced by the portfolio inclusion mechanism (underwriting/marketing), which makes each insurer’s portfolio a selected subpopulation. Relying on causal inference and a portfolio composition indicator, we characterize how portfolio composition bias affects common premium adjustments (unawareness, discrimination-free pricing, and transport-based corrective pricing), and we provide restrictive conditions under which portfolio and population adjustments coincide. We propose estimators to recover the fairness-adjusted premiums on the regulator-intended target population from selection-biased data, by using externally available information on the population marginal distribution of the prohibited attribute D. We study this scope mismatch from the policyholder’s perspective: we model the market premium faced by a newly entering policyholder (not yet assigned to any portfolio) as a mixture of insurer-specific premiums, weighted by the probability of being assigned to each insurer. Under this view, a pricing rule can satisfy a fairness criterion within each insurer’s portfolio yet produce direct or proxy discrimination in the market when portfolio inclusion depends on X and/or D. Finally, we show that enforcing portfolio-level balance on population-intended fair premiums can reintroduce portfolio composition bias, highlighting a regulatory trade-off between portfolio balancing and market-wide fairness. We focus on recoverability: which population-level fairness targets are identifiable from portfolio data, and what minimal external information is required to recover them.

A Scalable toolbox for exposing indirect discrimination in insurance rates

Our paper, ‘A Scalable toolbox for exposing indirect discrimination in insurance rates‘ with Olivier Côté and Marie-Pier Côté, is out.

Here is Alyssa Gambone  ()’s post on Linkedin

It’s time for one of my rare insurance related posts, though this one isn’t entirely off theme of my normal content. The CAS recently published a paper entitled ‘A Scalable toolbox for exposing indirect discrimination in insurance rates‘ by Olivier Côté, Marie-Pier Côté, and Arthur Charpentier that makes an incredibly important point as the actuarial profession goes deeper and deeper into machine learning and AI.  “In an unrealistic extreme, oracle insurers — capable of perfectly predicting both amount and timing of insurance claims — might charge each policyholder precisely their discounted future claim amount, questioning the very concept of insurance risk transfer.” I’m a big believer that in service of the “most accurate” rates (what the paper calls “actuarial fairness”, which is incredibly damning of our profession), we have lost our purpose, which is to ensure a wide ranging ability of society to take normal risks like driving a car, owning a home, or starting a business. Society is better when insurance is available and affordable, not when it is precisely accurate for the smallest groups possible. In service of the capitalistic goal of maximizing profits at all costs, we have found out that the costs might be our industry’s societal purpose and reason to exist. “As data granularity increases, so does the potential for actuarial justification in perpetuating [historic and socioeconomic] disparities.” Shame on our profession if it does.

There will be much more work published soon on those topics… Meanwhile, here was our abstract,

Exposé Chaire PARI, les trois piliers de l’équité en tarification

Mercredi matin (en France), après-midi (à Kyoto), nuit (à Montréal), je vais donner un exposé pour le séminaire mensuel de la chaire PARI, intitulé Un cadre de gouvernance à trois piliers pour une tarification équitable de l’assurance. J’y présenterais notre récent travail, publié justement par la Chaire PARI (document de travail 37), et également associé à un rapport publié par la Casualty Actuarial Society aux États-Unis (et présenté la semaine dernière par Olivier), A Scalable toolbox for exposing indirect discrimination in insurance rates”. Les slides sont en ligne.

CAS 2025 Annual Meeting, in Austin, Texas

This morning, Olivier Côté was invited to speak for one hour at the “CS-44 – Operationalizing Fairness in Actuarial Pricing: From Principle to Practice” session, at the CAS 2025 Annual Meeting, in Austin, Texas (US).

Fairness metrics often lack actuarial relevance and are expressed in abstract units, obscuring real-world consequences. For actuaries to intervene, proxy effects and unfair biases must be quantified in insurance-relevant terms: dollars and people. This session will present new research from the CAS Race and Insurance Pricing series, focusing on the unique challenge of establishing fairness in actuarial pricing. We argue that actuarial fairness, solidarity, and causality form the three dimensions of fairness in insurance. These give rise to a five-point spectrum of pricing benchmarks, each reflecting distinct fairness goals and trade-offs. We quantify the monetary impact of unfairness at both the policyholder and segment levels through a large-scale Québec auto insurance case study.

2025 CAS (Casualty Actuarial Science) Canada Connection

In less than a month, Olivier Côté will attend the  CAS Canada Connection, in Toronto.  He will speak in a session Operationalizing Fairness in Actuarial Pricing: From Principle to Practice

Fairness metrics often lack actuarial relevance and are expressed in abstract units, obscuring real-world consequences. For actuaries to intervene, proxy effects and unfair biases must be quantified in insurance-relevant terms: dollars and people. This session will present new research from the CAS Race and Insurance Pricing series, focusing on the unique challenge of establishing fairness in actuarial pricing. We argue that actuarial fairness, solidarity, and causality form the three dimensions of fairness in insurance. These give rise to a five-point spectrum of pricing benchmarks, each reflecting distinct fairness goals and trade-offs. We quantify the monetary impact of unfairness at both the policyholder and segment levels through a large-scale Québec auto insurance case study.

Learning objectives are (1) Describe three dimensions of fairness in insurance pricing: actuarial fairness, solidarity, and causality (2) Translate these dimensions of fairness into a spectrum of five pricing benchmarks (3) Diagnose and quantify potential unfairness at both individual and segment levels using actuarially meaningful metrics.

It will be based on our recent paper, A Scalable toolbox for exposing indirect discrimination in insurance rates”.

A Scalable toolbox for exposing indirect discrimination in insurance rates

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.

Un cadre de gouvernance à trois piliers pour une tarification équitable de l’assurance

Avec Marie-Pier et Olivier Côté, on a écrit un court article, un cadre de gouvernance à trois piliers pour une tarification équitable de l’assurance, publié par la chaire PARI.

L’assurance repose sur l’équilibre entre le risque individuel et la protection collective, mais les modèles contemporains de tarification fondés sur des données massives et des algorithmes opaques soulèvent des questions pressantes d’équité à l’égard des caractéristiques protégées prédéfinies. Alors que les standards actuariels visent une précision fondée sur le risque, les parties prenantes demandent de plus en plus une reddition de comptes et une responsabilisation éthique, une solidarité sociale et une protection contre la discrimination insidieuse. Nous soutenons que l’équité actuarielle, la solidarité et la causalité forment trois piliers distincts, complémentaires et essentiels pour une tarification équitable de l’assurance. Nous situons ces piliers dans des débats plus larges en éthique des affaires et en équité algorithmique, en les reliant aux traditions de justice distributive (Rawls, 1971; Sen, 1992), à l’éthique de l’information (Floridi, 2016; Nissenbaum, 2009), et à la théorie du partage de risque Arrow (1963). Nous soutenons que les trois piliers rendent explicites les compromis éthiques auxquels actuaires et assureurs sont confrontés lorsqu’ils déploient des modèles prédictifs. Aucun principe d’équité ne peut dominer sans détériorer les autres : l’équité actuarielle peut accentuer les disparités socioéconomiques, la solidarité peut compromettre l’efficience du marché, et la causalité, tout en cherchant de véritables effets de risque sans regard à la solidarité ou l’équité actuarielle, repose sur des postulats invérifiables qui peuvent entraver la puissance prédictive. En articulant ce cadre tridimensionnel, nous déplaçons l’équité d’une hypothèse implicite vers un objectif explicite de gouvernance, fournissant ainsi une perspective normative pour la gouvernance d’entreprise, l’élaboration de la réglementation et la reddition de comptes envers les parties prenantes dans l’industrie de l’assurance. Au-delà de la science actuarielle, ces trois piliers offrent un cadre généralisable pour évaluer l’équité dans d’autres domaines de décision algorithmique fondée sur le risque, de l’évaluation du pointage de crédit à la tarification des soins de santé.

Une version plus statistique, ou actuarielle, sera bientôt en ligne. Et je donnerai un exposé à la chaire PARI pour présenter ce papier.

Actuarial Research Conference in Toronto

From Tuesday to Friday, I will attend the 60th Actuarial Research Conference in Toronto. With Olivier and Marie-Pier Côté, we will give a series of talk on fairness and discrimination.

  • I will talk in an Invited Session on Artificial Intelligence in Insurance (as well as Marie-Pier Côté)
  • Olivier Côté will present in Session 1 – Bias in Assessing Financial Risk
  • With Olivier and Marie-Pier, we will present in one of the Casualty Actuarial Society Sponsored Sessions, Session 1A Scalable Toolbox for Exposing Indirect Discrimination in Insurance Rates

A fair price to pay: Exploiting causal graphs for fairness in insurance

Our paper “A fair price to pay: Exploiting causal graphs for fairness in insurance“, with Olivier Côté and Marie-Pier Côté just appeared in the Journal of Risk and Insurance,

In many jurisdictions, insurance companies are prohibited from discriminating based on certain policyholder characteristics. Exclusion of prohibited variables from models prevents direct discrimination, but fails to address proxy discrimination, a phenomenon especially prevalent when powerful predictive algorithms are fed with an abundance of acceptable covariates. The lack of formal definition for key fairness concepts, in particular indirect discrimination, hinders effective fairness assessment. We review causal inference notions and introduce a causal graph tailored for fairness in insurance. Exploiting these, we discuss potential sources of bias, formally define direct and indirect discrimination, and study the theoretical properties of fairness methodologies. A novel categorization of fair methodologies into five families (best-estimate, unaware, aware, hyperaware, and corrective) is constructed based on their expected fairness properties. A comprehensive pedagogical example illustrates the implications of our findings: the interplay between our fair score families, group fairness criteria, and discrimination.

Selection bias in insurance: why portfolio-specific fairness fails to extend market-wide

With Marie-Pier Côté and Olivier Côté, we recently upload a short note, selection bias in insurance: why portfolio-specific fairness fails to extend market-wide, now available on SSRN,

Fairness centres on people. In insurance, the scope of fairness should be the entire insured population, not solely an insurer’s clients. However, each insurance company’s portfolio represents a possibly skewed subsample. Models fit to these selection-biased data do not generalise well for the broader population of insureds. Two biases stem from portfolio composition: representation bias, when large prediction errors are made on individuals from subpopulations infrequently observed, and selection bias, when underwriting and marketing skew the portfolio away from the insured population. We examine how portfolio composition affects fair premium methodologies for mitigating direct and indirect discrimination on a protected attribute. We illustrate how unfairness mitigation based on a selection-biased portfolio does not yield a fair market from the perspective of insureds. Relying on causal inference and a portfolio composition indicator, we describe the selection mechanism and determine conditions under which each bias affects various fairness-adjusted premiums. We propose a method to recover the population-wide fairness-adjusted premiums from selection-biased data, by using a (third-party provided) unbiased estimate of the prohibited attribute distribution. We show that this approach effectively mitigates selection bias but leads to overall premiums that are not balanced. In a limiting case, we show that portfolio-specific fairness-aware premiums can lead to a market-wide unawareness strategy: portfolio composition opens the back door to proxy discrimination.

(to be continued…)

Talk at the 27th International Congress on Insurance: Mathematics and Economics

On Wednesday morning, I will be chairing our session “Discrimination-free Insurance Pricing” at the Insurance: Mathematics & Insurance Conference, in Chicago. With Olivier Côté, Lydia Gabric and Hong Beng Lim, we will be four speaker, just before lunch time. My talk will be a mix of recent work on quantifying and mitigating discrimination in scores (in insurance). Slides are available online.

 

WIM (Workshop in Insurance Mathematics) is back

After four year without it, the WIM is back. Last time, it was in February 2020. Tomorrow, Agathe and Olivier will present posters at the Workshop in Insurance Mathematics, a Concordia University.

Both posters will be on fairness and discrimination. Olivier Côté will present a poster on “Fairness in insurance enigma: exploring the maze of regulation

Agathe will present a poster on Equipy, “A Python Package for Sequential Fairness using Optimal Transport with Applications in Insurance