Talk on fairness and “differential pricing” in insurance

Tomorrow morning, I will give a talk on fairness, “differential pricing” and “price walking” in insurance, at the AXA Chief Actuary Meeting. Slides are available online.

I will get back on two reports published recently (that can be related to the recent EIOPA consultation)

The first one was the report by the Sweedish Finans Inspektionen, Fär lojala försäkringstagare betala mer?

and the study by the Central Bank of Ireland.

They get back on price walking, seen as a discrimination problem,

It found that pricing practices applied by insurance providers could result in unfair outcomes for some consumers in the private car and home insurance markets. These pricing practices include “price walking”, where consumers are charged higher premiums, relative to the expected cost, the longer they remain with an insurance provider. The Report indicates that the CBI considers this practice to be unfair, a point emphasised in the press release accompanying the report. The Report found that long term customers who stayed with the same insurer for 9 years or more, paid on average 14% more on private car insurance and 32% more on home insurance than the equivalent customer renewing for the first time.

They provide interesting graphs, with prices of motor insurance

as well as household insurance,

Insurance analytics: prediction, explainability and fairness (call for papers)

Call for papers: Insurance analytics: prediction, explainability and fairness –  special issue of the Annals of Actuarial Science. Submissions open 1 December 2022 and close 30 September 2023. With Kjersti Aas (Norwegian Computing Center & Norwegian University of Science and Technology (NTNU)), Ronald Richman (Old Mutual Insure & University of the Witwatersrand) and myself, serving as guest editors,

Scope of the special issue:
·        Methodological innovations in predictive analytics applied in insurance
·        Case studies of applications of machine learning and artificial intelligence within insurance
·        Methods for interpreting predictive models and designing inherently explainable models
·        Addressing discrimination and fairness considerations in insurance pricing and related applications
·        Algorithmic auditing and validation of predictive models in insurance
·        Software that enables the operationalisation of methods relating to the scope of the special issue
·        New developments with insurance applications in areas closely related to actuarial science

This special issue aims to capture leading academic thinking and industry applications in advanced insurance analytics. Submissions should demonstrate advances in at least one of the domains of predictive accuracy, explainable modelling and fairness. More…

Probabilités prédictives, pour 100% actuaires, et 100% data science

Ce jeudi, je participe (virtuellement) à un atelier sur les probabilités prédictives à la journée 100% actuaires, et 100% data science, de l’Institut des Actuaires, en France, avec Nicolas Marescaux et Florence Picard.

L’évènement n’étant pas offert en mode “hybride” je serais présent via une courte vidéo, qui sera transmise lors de l’atelier.

Je vais reprendre graphiquement un point que j’évoque régulièrement, à savoir la variabilité fondamentale qui existe lorsqu’on modéliser des évènements binaires, y compris si la vraie probabilité est connue. Dans un modèle Gaussien, si Y\sim\mathcal{N}(\mu,\sigma^2), même en connaissant (parfaitement) la moyenne \mu, Y-\mu est une variable, aléatoire, Y-\mu\sim\mathcal{N}(0,\sigma^2) qui peut avoir une petite variance, si \sigma est faible. Et dans un modèle de régression Y|X=x\sim\mathcal{N}(\mu_x,\sigma_0^2) avec \sigma_0^2\leq \sigma^2. Mais dans les GLM, avec les modèles de classification ou de Poisson, la variance ne diminue pas : si Y|X=x\sim\mathcal{B}(p_x), et la variance sera p_x(1-p_x) qui restera toujours non-nulle quand p_x\in(0,1).

L’autre point est que si on a une loi de Bernoulli, p ne peut être vraiment connu que si on a beaucoup d’observations, c’est la loi des grands nombres, sinon on a de la variabilité. Sur la figure ci-dessous, j’ai plusieurs niveaux de probabilité p, et je trace à gauche l’intervalle de “confiance” pour la fréquence, quand on n=100 observations, avec en bas la distribution de la fréquence. Par exemple, si p=15\%, avec une centaine d’observations, la fréquence a 90% de chances d’être entre 10\% et 20\%. Autrement dit, prédire une probabilité d’avoir un accident de 15.723\% n’a pas trop de sens. Au centre, le regarde la distribution de \overline{y}_n-p, et on voit qu’il reste une part non négligeable de variance. À droite, c’est la variation relative (\overline{y}_n-p)/p, qui varie en sens inverse par rapport à la variation absolue : si p est faible (disons 2\%), on s’écarte peu en valeur absolue (\pm 2\%) mais il n’est pas impossible (y compris avec n=100 observations) d’observer 2 fois trop de 1).

Regarder \overline{y}_n-p, c’est supposer qu’on peut connaître la vraie probabilité, et qu’on l’utilise : \overline{y} c’est la charge moyenne par années, et p, c’est la prime pure (annuelle). Donc \overline{y}_n-p, c’est la perte annuelle. Mais au lieu d’utiliser p, on peut imaginer qu’on mutualiser : par exemple ci-dessous, si p\in[0\%;4\%] on utilise la valeur moyenne (soit 2\%). On voit qu’on rajoute de la variabilité sur la distribution des pertes individuelle, d’autant plus qu’il y a peu de classes.

On en reparlera…

DataDay 2022 MAIF

Ce mercredi, je participerais au à la semaine DataDay 2022 de la MAIF, pour parler de données et de climat…

Je commencerais pas revenir (il s’agit d’un exposé grand public) sur les spécificités des différents types de données, en commençant par les données individuelles vs. les données temporelles

Dans le premier cas, on parlera surtout (dans les applications climatiques) de données spatiales

et dans le second cas, de séries temporelles,

On finira avec les données spatio-temporelles

Graduate Scholarships in Montréal (Canada)

We invite you to apply for a MSc or PhD grant, in the area of economics, statistics and data science, applied to insurance, starting mid-Spring 2023 (MSc) or Fall 2023 (PhD). We are seeking applications of students with a solid background in applied mathematics, theoretical economics, actuarial modeling, statistical learning and/or data science. Students interested in a PhD application (starting Fall 2023) are encouraged to apply for a Spring-Summer internship.

Topics Description :

Here is a list of possible topics: 

  • Game theory for insurance

keywords: game theory; dynamic games; insurance markets; bargain

Lemaire, J. (1980). A game theoretic look at life insurance underwriting.

Lemaire, J. (1991). Cooperative game theory and its insurance applications.

  1. Quantifying uncertainty in risk models

keywords: machine learning; neural networks; uncertainty; autocalibration; MCdropout; bayesian models

Gal, Y. (2016) Uncertainty in Deep Learning

Lahlou et al. (2022): Direct Epistemic Uncertainty Prediction 

  • Dimension reduction and interpretability

keywords: UMAP; T-SNE; Shapley; VAE

McInnes, L. &, Healy, J (2018) UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction,

Hinton & Roweis (2002) Stochastic neighbor embedding

v.d. Maaten & Hinton (2008):  Visualizing Data using t-SNE


  • Networks and risk sharing mechanism

keywords: networks; dynamic networks; P2P; altruism

Charpentier, A., Kouakou, L., Löwe, M., Ratz, P., & Vermet, F. (2021). Collaborative insurance sustainability and network structure

Abdikerimova & Feng (2022): Peer-to-peer multi-risk insurance and mutual aid 

  • Optimal transport for insurance

keywords: optimal transport; multivariate quantiles; risk measures; counterfactual; causal inference:

Carlier, G. (2010). Optimal Transportation and Economic Applications.

Additional Information :

Candidates will be located in the mathematics department at UQAM (Montréal). On some topics, industrial partnerships are associated with the project, and candidates will be working and interacting with either colleagues in Canada and France, or PhD students at UQAM.

The scholarship grants will be at a competitive level, with additional funding for travels (for PhD students) and local workshops and seminars (MSc and PhD)

Applications must be submitted electronically through email before February 1, 2023 to and consist of the following:

  • A (short) cover letter ;
  • A detailed curriculum vitae ;
  • Two contacts for recommendations

Climate risk, some slow long-term trend?

In most of the scenarios that talk about climate change, we are told about projections for 2050 or even 2100, time scales that are so far away that we have the illusion that the major risks will only be for “future generations“. And these scenarios evoke the possibility of a rise of 1, 2 or 4°C in several decades, a figure that should seem derisory when we are used to seeing temperatures vary by 10 or 20°C within the same day, by 15, 20 or even 30°C between winter and summer. In this context, how can we finally think seriously about climate risk?  Continue reading Climate risk, some slow long-term trend?