Category Archives: Research

A new GEE method to account for heteroscedasticity using asymmetric least-square regressions

Our paper, with Amadou Barry and Karim Oualkacha, a new GEE method to account for heteroscedasticity using asymmetric least-square regressions is now published in the Journal of Applied Statistics

Generalized estimating equations (GEE) are widely used to analyze longitudinal data; however, they are not appropriate for heteroscedastic data, because they only estimate regressor effects on the mean response – and therefore do not account for data heterogeneity. Here, we combine the GEE with the asymmetric least squares (expectile) regression to derive a new class of estimators, which we call generalized expectile estimating equations (GEEE). The GEEE model estimates regressor effects on the expectiles of the response distribution, which provides a detailed view of regressor effects on the entire response distribution. In addition to capturing data heteroscedasticity, the GEEE extends the various working correlation structures to account for within-subject dependence. We derive the asymptotic properties of the GEEE estimators and propose a robust estimator of its covariance matrix for inference (see our R package, Our simulations show that the GEEE estimator is non-biased and efficient, and our real data analysis shows it captures heteroscedasticity.

Predicting Drought and Subsidence Risks in France

New paper with Molly James and Hani Ali, now available on

The economic consequences of drought episodes are increasingly important, although they are often difficult to apprehend in part because of the complexity of the underlying mechanisms. In this article, we will study one of the consequences of drought, namely the risk of subsidence (or more specifically clay shrinkage induced subsidence), for which insurance has been mandatory in France for several decades. Using data obtained from several insurers, representing about a quarter of the household insurance market, over the past twenty years, we propose some statistical models to predict the frequency but also the intensity of these droughts, for insurers, showing that climate change will have probably major economic consequences on this risk. But even if we use more advanced models than standard regression-type models (here random forests to capture non linearity and cross effects), it is still difficult to predict the economic cost of subsidence claims, even if all geophysical and climatic information is available.

Collaborative Insurance Sustainability and Network Structure

Our joint paper, with Lariosse Kouakou, Matthias Löwe, Philipp Ratz and Franck Vermet, entitled “Collaborative Insurance Sustainability and Network Structure” is now available on Arxiv,

The peer-to-peer (P2P) economy has been growing with the advent of the internet, with well known brands such as Uber or Airbnb being examples thereof. In the insurance sector the approach is still in its infancy, but some companies have started to explore P2P-based collaborative insurance products (eg. Lemonade in the U.S. or Inspeer in France). The actuarial literature only recently started to consider those risk sharing mechanisms, as in Denuit and Robert (2020) or Feng et al. (2021). In this paper, describe and analyse such a P2P product, with some reciprocal risk sharing contracts. Here, we consider the case where policyholders still have an insurance contract, but the first self-insurance layer, below the deductible, can be shared with friends. We study the impact of the shape of the network (through the distribution of degrees) on the risk reduction. We consider also some optimal setting of the reciprocal commitments, and discuss the introduction of contracts with friends of friends to mitigate some possible drawbacks of having people without enough connections to exchange risks.

United As One, IME 2021

Next week, colleagues from the University of Illinois Urbana-Champaign and the Pennsylvania State University in the United States, Ulm University in Germany, and the University of New South Wales (UNSW Sydney) in Australia organize the 24th International Congress on Insurance: Mathematics and Economics, aka IME2021. I will present our joint work, with Michel Denuit and Julien Trufin, Autocalibration for Insurance Pricing with Machine Learning, Philipp Ratz will present our joint work on peer-to-peer insurance model. I will also chair some sessions, and participate to a round table on Thursday morning (Montréal time).

ASTIN Online Colloquium

Next week, I will present at the 2021 ASTIN Online Colloquium (online, of course, it will not be possible to meet in person, in Florida). I will present the joint paper with Michel Denuit and Julien Trufin, Autocalibration for Insurance Pricing with Machine Learning. Earlier on Wednesday, Philipp Ratz will present our work Collaborative Insurance Sustainability and Network Structure.

Insurance against Natural Catastrophes: Balancing Actuarial Fairness and Social Solidarity

Our research paper, Insurance against Natural Catastrophes: Balancing Actuarial Fairness and Social Solidarity, with Molly James and Laurence Barry, is now published in the Geneva Papers on Risk and Insurance.

Natural disasters offer a special case for the study of private and public insurance mix. Indeed, the experience accumulated over the past decades has made it possible to transform poorly known hazards, long considered uninsurable, into risks that can be assessed with some precision. They exemplify however the limits of the risk-based premiums method, as it might imply unaffordability for some. The French scheme reflects such ideas and offers a wide coverage for moderate premiums to all, but is shaken by climate change: we show that some wealthier areas, that were not perceived as “at risk” in the past, have become exposed to submersion risk in the future. This singularly makes some well-off properties the potential main beneficiaries of a scheme that was historically thought to protect the worst-off. Acknowledging that some segmentation might become desirable, we examine several models for flood risk and the disparity in premiums they entail.

Reinforcement Learning in Economics and Finance, a state-of-the-art

Our joint paper, with Romuald Elie and Carl Remlinger entitled Reinforcement Learning in Economics and Finance just appeared in Computational Economics,

Reinforcement learning algorithms describe how an agent can learn an optimal action policy in a sequential decision process, through repeated experience. In a given environment, the agent policy provides him some running and terminal rewards. As in online learning, the agent learns sequentially. As in multi-armed bandit problems, when an agent picks an action, he can not infer ex-post the rewards induced by other action choices. In reinforcement learning, his actions have consequences: they influence not only rewards, but also future states of the world. The goal of reinforcement learning is to find an optimal policy — a mapping from the states of the world to the set of actions, in order to maximize cumulative reward, which is a long term strategy. Exploring might be sub-optimal on a short-term horizon but could lead to optimal long-term ones. Many problems of optimal control, popular in economics for more than forty years, can be expressed in the reinforcement learning framework, and recent advances in computational science, provided in particular by deep learning algorithms, can be used by economists in order to solve complex behavioral problems. In this article, we propose a state-of-the-art of reinforcement learning techniques, and present applications in economics, game theory, operation research and finance.

Big data, the tech giants, and insurance

A few months ago, I published a short article, Big data, the tech giants, and insurance, in the Annales de Mines. The original article was in French, but the Editors shared an English version,

Technology and insurance companies seem like polar opposites in every possible way. The tech giants, agile and fast-acting, are obsessed with the future, whereas insurers, conservative and reflexive, are fascinated with the data that the tech giants collect. However these two sectors are now eyeing each other and have started forming partnerships as they come to understand that, in both cases, their core business is data.

to be continued…

Assurances et véhicules autonomes

Lundi matin, j’interviendrai dans un séminaire organisé par Stève Bernardin, sur le thème  “assurances et véhicules autonomes”, avec comme autres participants Philippe Talleux, Romain Cros, David Zuby et Jonathan Charak. En guise d’introduction, je peux renvoyer vers deux articles que nous avions écrit avec Rodolphe Bigot, Repenser la responsabilité, et la causalité et surtout Quelle responsabilité pour les algorithmes ?

Principal Component Analysis: A Generalized Gini Approach

Our paper, with Stéphane Mussard and Téa Ouraga, entitle Principal Component Analysis: A Generalized Gini Approach is finally out in the European Journal of Operations Research.

A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent to the Gini PCA. It is also proven that the dimensionality reduction based on the generalized Gini correlation matrix, that relies on city-block distances, is robust to outliers. Monte Carlo simulations and an application on cars data (with outliers) show the robustness of the Gini PCA and provide different interpretations of the results compared with the variance PCA.

IRE (HEC) – CREEI Seminar, HEC Montréal, on Monday

This Monday, I will give a talk at the IRE (HEC) – CREEI Seminar, at HEC Montréal. I will have one hour to present our work, with Olivier Cabrignac and Ewen Gallic, on “Modeling Joint Lives within Families