Category Archives: Research

Economics, Publications

Discounting the Future?

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this post is written with Béatrice Cherrier (Research Director, CNRS-ENSAE / CREST)

The first lessons in insurance and financial mathematics address discounting and the value of time, borrowing Christian Gollier’s expression, because insurers must account for this temporal aspect in medium-term annuity calculations. But do these discounting calculations, used for centuries to reflect individual decisions (of policyholders, investors, companies), still make sense when used to guide public policy decisions with long-term consequences, like climate policies?

When Kenneth Arrow joined the IPCC team in 1993, he expressed this concern to the coordinator of certain chapters: discounting in climate economics is as necessary as it is controversial. He wrote: “Your outline is very complete, with one exception. There needs to be discussion of discount rates. To a considerable extent, suggested policies require present costs (reduced carbon consumption) to prevent future disutilities and costs. Clearly, the tradeoff between present and future is very important, controversial though it be” (Cherrier and Duarte 2024).

The history of this transfer of a mathematical tool from the individual to the collective dimension since the 1930s, summarized here, is rich with lessons.
Continue reading Discounting the Future? →

Publications

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

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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…)

Seminar

Talk at the Financial Conduct Authority, UK

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This morning (Montréal time), I will give a talk for the Financial Conduct Authority in London, in the UK, on “Demystify fairness and discrimination in insurance, and avoid some pitfalls“.

What’s unique about insurance is that even statistical discrimination, which by definition is devoid of malicious intent, poses significant challenges. Because, on the one hand, policymakers would like insurers to treat their policyholders equally, without discrimination based on race, gender, age or other characteristics, even if it could make (statistical) sense to (indirectly) discriminate. On the other hand, at the core of actuaries’ activities lies discrimination, between risky and non-risky policyholders. And this risk is often statistically correlated with sensitive characteristics that regulation would like to prohibit insurers from taking into account. The analysis of possible discrimination in decision rules, whether human or algorithmic, is an old subject. Most of the concepts date back at least to the 50s, but recent developments in artificial intelligence have brought these issues back into the spotlight. Massive data facilitate statistical or proxy discrimination, and black-box algorithms do not facilitate understanding. Not to mention the various regulations that make it difficult to collect sensitive information, and ultimately test whether decisions can be discriminated against, especially indirectly.

Publications

How to Go Beyond the Coldness of Numbers and Take Action?

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 This article was written with Nicolas Marescaux, originally in French.

Today, our modern life relies largely on numbers. They guide most collective decisions and many individual choices. For Lord Kelvin [1], “If you cannot measure it, you cannot improve it.” In other words, to make a good decision, you must first measure well. But is that enough? IPCC reports have been compiling data and figures for decades, announcing a short-term catastrophe. And yet, nothing happens. “The modern man scorns imagination,” stated Stéphane Mallarmé in 1897. Isn’t it this subjectivity of our imagination that could save us? Continue reading How to Go Beyond the Coldness of Numbers and Take Action? →

Publications

Comment dépasser la froideur des chiffres, et agir ?

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Cet article a été écrit avec Nicolas Marescaux,

Aujourd’hui, notre vie moderne repose en grande partie sur les chiffres. Ils orientent la plupart des décisions collectives et de nombreux choix individuels. Pour Lord Kelvin [1], « If you cannot measure it, you cannot improve it. » Autrement dit, pour bien décider, il faudrait d’abord bien mesurer. Mais est-ce suffisant ? Les rapports du GIEC compilent des données et des chiffres annonçant, depuis plusieurs décennies, une catastrophe à court terme. Et pourtant, rien ne se passe. « Le moderne dédaigne d’imaginer » affirmait Stéphane Mallarmé en 1897. N’est-ce pas cette subjectivité de notre imaginaire qui pourrait nous sauver ?
Continue reading Comment dépasser la froideur des chiffres, et agir ? →

Seminar

Perspective causale sur les discriminations directes et indirectes liées aux caractéristiques sensibles dans les modèles prédictifs en assurance

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Olivier Côté donnera un exposé “Perspective causale sur les discriminations directes et indirectes liées aux caractéristiques sensibles dans les modèles prédictifs en assurance” au séminaire étudiant de l’IID intitulé modèles causaux et inférence causale en médecine et assurance, cet après midi

L’équité envers les assurés est un enjeu central pour le secteur de l’assurance. Les assureurs reposent largement sur les données personnelles pour plusieurs décisions automatisées. Dans ce travail, nous explorons la tarification équitable en assurance à travers une perspective causale, en mettant l’accent sur les discriminations directes et indirectes liées aux variables sensibles définies et observées. Nous analysons les mécanismes par lesquels ces variables influencent la tarification et proposons une catégorisation des méthodologies équitables en cinq familles, chacune présentant des propriétés claires en matière d’équité. Le raisonnement causal permet de représenter les biais, de clarifier les hypothèses concernant le mécanisme générateur de données, et de distinguer le signal de chaque variable par rapport aux variables sensibles.

Les outils développés guideront les spécialistes du secteur de l’assurance vers de meilleures pratiques en équité algorithmique.

Seminar

Algorithmic fairness with optimal transport: quantifying counterfactual fairness and mitigating group fairness

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This Friday, I will be in Laval University, in Québec, to give a talk at the Statlab annual day.

In this talk, we present two complementary approaches to addressing fairness in algorithmic decision-making, regarding individual and group fairness. First, we use Wasserstein barycenters to obtain (strong Demographic Parity) with one or multiple sensitive features. Our method provides a closed-form solution for the optimal, sequentially fair predictor, enabling possible interpretation of correlations between sensitive attributes. Then, we introduce a novel method that links two existing counterfactual approaches: causal graph-based adaptations (Plečko and Meinshausen, 2020) and optimal transport (De Lara et al., 2024). By extending “Knothe’s rearrangement” (Bonnotte, 2013) and “triangular transport” (Zech and Marzouk, 2022) to probabilistic graphical models, we propose a new group framework, termed sequential transport, which we apply to the problem of individual fairness. Theoretical foundations are established, followed by numerical demonstrations on synthetic and real datasets.

Slides are available online.

Research

SCOR Project Newsletter #2

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The second newsletter, related to the SCOR research project is now available. It is a brief summary of the second six months block, from April till the end of September (the first one is available here).

As explained, over the past six months, we have had several interns, including Noé Bosc-Haddad, Florent Crouzet, Julien Siharath, Ana María Patrón Piñerez and Cassandra Mussard, the visit of Laurence Barry and Fei Huang, Philipp Ratz and Samuel Stocksieker defended their PhD, François Hu finished his postdoctoral fellowship, while Marouane Il Idrissi and Arsene Zotsa just arrived, Agathe Fernandes Machado and Olivier Côté (co-supervised with Ewen Gallic and Marie-Pier Côté) finished their PhD courses and are now 100% on their research… We wrote papers, gave talks… Thank you to all those who have supported us, and continue to support us. At least two more years to work on insurance and predictive models, fairness, calibration, discrimination, trust, explainability, interpretability, market equilibria, competition, generative models, and so much more… We’ve still got a lot of work to do, and plenty of enthusiasm!

Conferences

Colloque, au Centre Culturel International de Cerisy, en France

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Je serai pour les 6 prochains jours au Centre Culturel International de Cerisy, pour un colloque sur “l’assurance face à ses ruptures“. Au programme (13/9) histoire de l’assurance, (14/9) la financiarisation, (15/9) les données massives, (16/9) le changement climatique et (17/9) le rôle de l’État. Je ferais une intervention dimanche matin, sur le thème Certitudes collective et incertitudes individuelles, les données massives changent-elles la donne ?

Dans cette intervention, nous commencerons par un détour historique et sociologique en revenant sur les travaux d’Émile Durkheim et Max Weber. Ces chercheurs ont montré que bien que les actions individuelles puissent être imprévisibles, les comportements collectifs suivent des schémas réguliers. En agrégeant les actions individuelles, nous observons des régularités au sein de groupes plus larges, une idée illustrée par la prédictibilité du suicide dans le contexte des données massives. Ensuite, nous aborderons les réflexions de Herbert Simon et sa théorie de la rationalité limitée, suggérant que malgré les limites cognitives des individus, les rendant individuellement imprévisibles, des modèles prévisibles émergent dans la prise de décision globale. Nous explorerons ensuite des questions épistémologiques en discutant l’interprétation fréquentiste des probabilités, laquelle requiert la répétition pour être quantifiée, et la difficulté d’associer une probabilité à un événement unique. La réponse bayésienne, qui interprète les probabilités comme des croyances ou des scores, complique la relation avec l’équité actuarielle. Nous questionnerons la calibration des modèles et l’interprétation des scores à travers des exemples simples, tels que “avoir 70% de chances qu’une opération militaire réussisse” ou “avoir 70% de chances de pluie entre 14 et 15 heures”. Enfin, nous conclurons en prenant en compte le caractère temporel de la prévision: prévoir un accident 15 minutes avant qu’il ne survienne n’est pas équivalent à le prévoir un an à l’avance.

Les slides sont en ligne. Sinon Le Monde, quotidien français, publiait un portrait des colloques (organisés depuis 1952) cet été, il y a un mois,

Seminar

“Mathematical Foundations of AI” day at the Sorbonne center for artificial intelligence

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On Thursday 12th, I will attend the Mathematical Foundations of AI day, organized by the DATAIA Institute and SCAI (Sorbonne Center for Artificial Intelligence), in association with several scientific societies (namely, the Fondation Mathématique Jacques Hadamard (FMJH), the Fondation Sciences Mathématiques de Paris-FSMP, the MALIA group of the Société Française de Statistique and the Société Savante Francophone d’Apprentissage Machine (SSFAM)).

Slides are now online.

In this talk, we present two complementary approaches to addressing fairness in algorithmic decision-making through the lens of counterfactual reasoning and optimal transport, both in individual and group fairness. First, we introduce a novel method that links two existing counterfactual approaches: causal graph-based adaptations (Plečko and Meinshausen, 2020) and optimal transport (De Lara et al., 2024). By extending “Knothe’s rearrangement” (Bonnotte, 2013) and “triangular transport” (Zech and Marzouk, 2022) to probabilistic graphical models, we propose a new group framework, termed sequential transport, which we apply to the problem of individual fairness. Theoretical foundations are established, followed by numerical demonstrations on synthetic and real datasets. Building on this, we extend the discussion to algorithmic fairness in the presence of multiple sensitive attributes. While traditional fairness frameworks focus on eliminating bias with respect to a single sensitive variable, their effectiveness diminishes with multiple sensitive characteristics. To address this, we propose a sequential fairness framework based on multi-marginal Wasserstein barycenters, generalizing Strong Demographic Parity to handle multiple sensitive features. Our method provides a closed-form solution for the optimal, sequentially fair predictor, enabling interpretation of correlations between sensitive attributes. Furthermore, we introduce an approximate fairness framework that balances risk and unfairness, allowing for prioritization of fairness across specific attributes. Both approaches are supported by comprehensive numerical experiments on synthetic and real-world datasets, showcasing the practical efficacy of these methods in promoting fair decision-making. Together, they provide a robust framework for addressing fairness in complex, multi-attribute settings while preserving interpretability and flexibility.

References are given below

  1. we will discuss further counterfactual fairness, initiated in Optimal Transport for Counterfactual Estimation: A Method for Causal Inference, and the more recent paper Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness 
  2. we will discuss Wasserstein barycenters with multiple sensistive attributes, A Sequentially Fair Mechanism for Multiple Sensitive Attributes

[added on Sept 13th] Thanks (on the right) for this nice picture with .

Conferences, Trip

European Actuarial Journal Conference (in Lisbon)

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Next week, I will be at the European Actuarial Journal Conference, at the Lisbon School of Economics and Business, EAJ’24.

I will give a talk on calibration of actuarial models, based on our recent paper with Agathe Fernandes Machado, Emmanuel Flachaire, Ewen Gallic and François Hu, mainly “Probabilistic Scores of Classifiers, Calibration is not Enough” (as well as recent work on recalibration). Slides are available.

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to ensure alignment between predicted probabilities and actual outcomes. However, when score heterogeneity deviates from the underlying data probability distribution, traditional calibration metrics lose reliability, failing to align score distribution with actual probabilities. In this study, we highlight approaches that prioritize optimizing the alignment between predicted scores and true probability distributions over minimizing traditional performance or calibration metrics. When employing tree-based models such as Random Forest and XGBoost, our analysis emphasizes the flexibility these models offer in tuning hyperparameters to minimize the Kullback-Leibler (KL) divergence between predicted and true distributions. Through extensive empirical analysis across 10 UCI datasets and simulations, we demonstrate that optimizing tree-based models based on KL divergence yields superior alignment between predicted scores and actual probabilities without significant performance loss. In real-world scenarios, the reference probability is determined a priori as a Beta distribution estimated through maximum likelihood. Conversely, minimizing traditional calibration metrics may lead to suboptimal results, characterized by notable performance declines and inferior KL values. Our findings reveal limitations in traditional calibration metrics, which could undermine the reliability of predictive models for critical decision-making.