
Today, I will give the second lecture of the 数学・数理科学グローバル特別講義6について, at Kyoto University. The course will be located at 3号館127大会議室. Lecture notes are available online.

Today, I will give the second lecture of the 数学・数理科学グローバル特別講義6について, at Kyoto University. The course will be located at 3号館127大会議室. Lecture notes are available online.
My upcoming lectures at Kyoto University as part of the Global Special Lecture Series in Mathematics and Mathematical Sciences (No. 6) is now on the agenda: November 4, 5, 10, 11, and 13, 2025, from 9:30 till 11:30, at the Graduate School of Science, Kyoto University.
It will be one “Fairness and Distribution in Insurance – An Actuarial Perspective”. We will explore how fairness, risk sharing, and distributional concerns intersect with actuarial science and insurance, providing both theoretical insights and practical implications.
I am truly honored to contribute to this international program and look forward to engaging with students and colleagues in Kyoto.

The afternoon, we will have the first course on Inequalities. Slides are available from here.

Tomorrow morning, I will give a crash course on risk measures at Louvain-la-Neuve, in Belgium. This is a crash course of PhD students (and researchers) with a long introduction on the univariate static framework (and some mathematical tools that will be interesting later on, such as the Fenchel transform and more generally on convexity, as well as some results on optimal transport). I will also mention what was obtained in decision theory, inspired by Itzhak Gilboa‘s Theory of Decision under Uncertainty. Then I will mention extensions to derive multiple risk measures, based on Marc Henry and Alfred Galichon‘s work. Finally, I will conclude by introducing the difficulty to derive dynamic risk measures.
The slides are based on a document I am still working on. And unfortunately, the deeper I get to explain the roots of the axioms, or the assumptions, the more papers I discover (and I need to read, and understand). So I guess I will need some time to finalize my survey. Note that I decided to skip details on technical issues when working on , and the weak topology on the dual of
. I will try to add additional references in the notes, but I wanted the slides to be as simple as possible. I also want to add more connections with statistical results, such as Neyman Pearson’s lemma, for instance (as mentioned in a paper by Alexander Schied). All my apologies for the typos, too.
Short course on Measuring and Covering Catastrophic Risks at the Maresias Conference in Sao Paulo, April 2009. Slides are now online.
There has been recently a large interest in catastrophic risks, especially following hurricane seasons in 2004 and 2005. But measuring those risks and providing an appropriate cover might be difficult. In this course, we will first describe those risks, especially climate risks (or climate related), man based risks (large fires or business interuption), and mortality risks. For those risks, we will also discuss possible covers, from classical (re)insurance to securitization (cat or mortality bonds) or insurance-linked securities (cat options). As we will see, the pricing of those products can simply be related to the choice of a risk measure. We will then discuss risk measures for large risks, and conclude with the aggregation issue.


Two examples of natural catastrophes securitization will be studied carefully

The dataset used in this example was kindly provided by Dr. Miguel A. Santoyo (here)
