# Brief talk on non-diversification of extreme risks, for France Stratégie

Tomorrow, I was invited to give a (brief) talk at our working group, at France Stratégies, on (non) diversification of extreme risks. Slides are online, and results are related to recent papers by Paul Embrechts and Ruodu Wang. More precisely, here are some references

But first, before discussing large risks, I need to get back (quickly) on the Pareto distribution,

To visualize Pareto tails, one can consider the Pareto plot. If points are on a straight line with (negative) slope $\alpha$, then observations are Pareto distributed, with tail index precisely $\alpha$. Depending on the slope (compared with -1), risks have either finite or infinite mean.

Infinite mean is not that common actually. It is hard to visualize what it means, actually because for any (finite) $n$, the empirical average $$\displaystyle{\overline{x}=\frac{1}{n}\sum_{i=1}^nx_i}$$ always exists. To visualize what’s going on, we can plot the ratio $\max\{x_i\}$ over the sum. That could be related to the concept of “top share” in inequality.

On the left, risks with finite variance (and of course finite mean). In the middle, infinite variance by finite mean. After a while, it is quite rare to have the maximum weighting for more than 1% in the total sum. With infinite mean, on the right (not too far from the limit, since $\alpha$ is here 0.95 – finite mean means that $\alpha$ exceeds one).

Now, if we get back to risks and insurance, recall basic things on stochastic dominance,

Then we have the following results (that is actually the most important slide)

I did include a slide with the mathematical proof (that is quite lovely actually, and straightforward)

# Oaxaca-Blinder decomposition of changes in means and inequality

Our paper, Oaxaca-Blinder decomposition of changes in means and inequality: A simultaneous approach, with Emmanuel Flachaire, was just published in the Economics Bulletin,

In this paper, we show that a decomposition of changes in inequality, with the mean log deviation index, can be
obtained directly from the Oaxaca-Blinder decompositions of changes in means of incomes and log-incomes. It allows practitioners to conduct simultaneously empirical analyses to explain which factors account for changes in means and in inequality indices between two distributions with strictly positive values.

Note that the Oaxaca-Blinder decomposition actually originated in the work of Evelyn Kitagawa in the 1950’s, to quantify gender discrimination in labour economics.

Kitagawa, E. M. (1955). Components of a difference between two rates. Journal of the American Statistical Association, 50 (272), 1168–1194.

# Workshop on fairness and discrimination in insurance (registration is open)

Almost two years ago, on May 13th 2022, we organized a Workshop on fairness and discrimination in insurance, JEDA’22, at Laval University (in Québec city), with Marie-Pier Côté.

It was a beautiful sucess, with a lot of persons in person, for one of the first event post-pandemic. The second workshop (JEDA’24) will be organized in less than a month, on May 16th.

Registrations are open ! We will have in the room Fei Huang (UNSW Sidney), David Schraub (Chicago Actuarial Association), Marie-Ève Lainez, Autorité des marchés financiers), Laurence Barry (Chaire PARI), Agathe Fernandes Machado (UQÀM) Mallika Bender (Casualty Actuarial Society), Christopher Cooney (TD Insurance) and Olivier Côté (Université Laval).

# Foundations of Data Science (Lancaster University)

With Russell Davidson, we will give a short course on Foundations of Data Science, at Lancaster University (actually, online), in the Data Science and Econometrics program.

# Groupe de travail, dimension territoriale dans la mutualisation des risques climatiques

Demain matin, on m’a demandé d’intervenir au groupe de travail “mutualisation des risques” de France Stratégie. A priori, j’interviendrais dans la discussion sur “Comment mutualiser les risques climatiques entre territoires ? “, et j’ai préparé quelques slides sur la base de mes travaux depuis une petite vingtaine d’année (ma participation au groupe de travail du Commissariat au Plan sur L’État et l’assurance des risques nouveaux remonte à 2005…).

# Great workshop in Corsica

At the Institut d’Etudes Scientifiques (IES), in Cargèse, Corsica, we had an amazing workshop on optimal transport.

It is now time to wrap-up all the notes taken, and try to get keep in touch with some colleagues I want to work with…

# Éclipse solaire…

(sur le campus de McGill, photo volée à ma fille)

# Journée de la recherche en sciences

Ce jeudi, c’est la journée de la recherche en sciences, sur le campus de la faculté. Agathe a présenté (rapidement) ses travaux récents sur l’équité et la calibration de modèles prédictifs !