
Le dernier numéro de Risques est sorti.



Tout nouveau tout chaud, le dernier numéro de l’Actuariel est paru, avec en particulier un article Open finance : Big bang annoncé dans l’assurance pour lequel j’avais eu long entretien. Au delà de quelques idées qu’on retrouve ici ou là, je peux mentionner une petite phrase, qui semble avoir retenu l’attention…
« Le débat est posé de manière sournoise en faisant croire aux citoyens qu’ils bénéficieront de produits plus personnalisés, sans rappeler que l’assurance est bien souvent un jeu à somme nulle et que si certains paient moins cher, cela signifie que d’autres paient plus » indique Arthur Charpentier, professeur à l’Université du Québec à Montréal et actuaire agrégé.

Our paper optimal vaccination policy to prevent endemicity: a stochastic model, written with Félix Foutel-Rodier and Hélène Guérin was just published in the Journal of Mathematical Biology
We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and subsequent immunity, is introduced, considering stochasticity at the individual level. By letting the population size to go to infinity, we derive a set of equations describing the large scale behavior of the epidemic. The analysis of the model’s equilibria reveals a criterion for the existence of an endemic equilibrium, which depends on the rate of immunity loss and the distribution of time between booster doses. The outcome of a vaccination policy in this context is influenced by the efficiency of the vaccine in blocking transmissions and the distribution pattern of booster doses within the population. Strategies with evenly spaced booster shots at the individual level prove to be more effective in preventing disease spread compared to irregularly spaced boosters, as longer intervals without vaccination increase susceptibility and facilitate more efficient disease transmission. We provide an expression for the critical fraction of the population required to adhere to the vaccination policy in order to eradicate the disease, that resembles a well-known threshold for preventing an endemic state with an imperfect vaccine. We also investigate the consequences of unequal vaccine access in a population and prove that, under reasonable assumptions fair vaccine allocation is the optimal strategy to prevent endemicity.

Our paper, Data Augmentation with Variational Autoencoder for Imbalanced Dataset, with Samuel Stocksieker and Denys Pommeret is now online on ArXiv.
Learning from an imbalanced distribution presents a major challenge in predictive modeling, as it generally leads to a reduction in the performance of standard algorithms. Various approaches exist to address this issue, but many of them concern classification problems, with a limited focus on regression. In this paper, we introduce a novel method aimed at enhancing learning on tabular data in the Imbalanced Regression (IR) framework, which remains a significant problem. We propose to use variational autoencoders (VAE) which are known as a powerful tool for synthetic data generation, offering an interesting approach to modeling and capturing latent representations of complex distributions. However, VAEs can be inefficient when dealing with IR. Therefore, we develop a novel approach for generating data, combining VAE with a smoothed bootstrap, specifically designed to address the challenges of IR. We numerically investigate the scope of this method by comparing it against its competitors on simulations and datasets known for IR.
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?
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.

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.
This week-end (🥳) I will attend the 39th Annual Meeting of the Canadian Econometrics Study Group (CESG), in Toronto, Ontario on October 25-27, 2024. I will give a talk on calibration, based on recent work, with Agathe Fernandes Machado, Ewen Gallic, Emmanuel Flachaire and François Hu. Slides are available online.

Le dernier numéro de la revue Risques est sorti.
avec plusieurs articles sur les “risques extrêmes”

Dans la dernière section, on y retrouve mon court article Peut-on diversifier des risques extrêmes?

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?
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 ?
Our paper Post-Calibration Techniques: Balancing Calibration and Score Distribution Alignment, will be presented at the NeurIPS workshop on Bayesian Decision-making and Uncertainty, that will take place in Vancouver, mid December. Agathe will be there to present it…

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.
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.

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!