Institut de recherche mathématique avancée

Résumé : A common assumption in classical risk theory is the independence between claim frequency and severity. However, this often fails in practice, especially when subtle or nonlinear dependencies are present. This study analyzes a real-world dataset comprising 15,665 claims from housing and liability insurance contracts, recorded between 01/01/2015 and 31/12/2019, provided by an anonymous insurer. Unlike most literature focused on automobile insurance, our data allow us to explore dependence in less-studied lines of business, which pose unique challenges. We investigate the presence and nature of dependence between frequency and severity, and how this relationship evolves over time and across insurance types. Our approach combines parametric and nonparametric methods: we fit Poisson-Inverse Gaussian, Negative Binomial, Weibull, and Log-Normal distributions to the marginals, and apply copula-based techniques to assess joint behavior. Using pseudo-observations, we estimate empirical copulas, visualize joint densities, and perform statistical tests of independence and equality (KcopTest), which reveal a structural break in housing insurance in 2016. Results indicate strong positive dependence in liability insurance. In housing insurance, we find near-independence in most years, but a weak and significant negative dependence in 2016. Finally, GAMLSS models confirm diverging patterns: in liability insurance, severity increases with frequency; in housing insurance, it decreases, in contrast to findings by Garrido (2016). We discuss implications for pricing, reserving, and solvency assessment under dependence.

Résumé : In this talk, I will first introduce Anosov flows and their significance in the study of hyperbolic dynamical systems and topology of 3-manifolds. A fundamental question is whether a given 3-manifold supports only finitely many Anosov flows up to orbit equivalence. A powerful construction method involves gluing “building blocks” of flows. I will present a finiteness result for Anosov flows obtained through this procedure. I will also explain how this result, combined with classification results, contributes to an ongoing joint work with Thomas Barthelmé on the finiteness problem for Anosov flows on 3-manifolds.

Résumé : The diversity among galaxies showcases a broad spectrum of mass and angular momentum distributions. During formation, gravitational forces drive these celestial bodies to collapse, acquiring angular momentum via torques. Thanks to dissipation, the result post virialization is typically a flattened rotating structure. Understanding how this geometry and kinematics affects the response of galaxies is important to explain their long-term evolution.
Such endeavor has been attempted through costly N-body simulations. However, a worthy alternative is to follow the path of Kalnajs and compute the linear response of such systems. Historically, the complexity of studying generic three-dimensional systems posed significant challenges (six-dimensional phase space fully coupled via self-gravity). However, modern computers can now model more complex shapes or kinematics, opening the prospects of also extending our understanding beyond the spherical or razor thin geometries.

About the speaker :
Kerwann Tep is a postdoctoral researcher at the Observatoire astronomique de Strasbourg working on the exascale project. Prior to joining the observatory, he did his PhD at the Institute d'astrophysique de Paris and a postdoctoral stay at the University of North Carolina at Chapell Hill working on Galactic dynamics and stability of gravitational systems

Résumé : I will first introduce the moduli spaces of Higgs bundles that appear in the Hausel-Thaddeus topological mirror symmetry conjecture, present its different proofs and generalisations. In particular I will explain the p-adic integration approach of Groechenig, Wyss and Ziegler. Finally, I will present my result, which is a generalisation beyond the original coprime case of the key intermediate step of this approach, which we call a non-archimedean topological mirror symmetry.

Résumé : Numerous PDEs can be written of the form y'=Ay+f(y) where A is a linear operator and f represents a nonlinearity. To deal with this kind of PDE, we use to treat first the linear case which comes in the form y'=Ay. The aim of the talk will be to study the issue of solving such PDEs using the notion of semigroups. I will introduce the notion of unbounded operators on Hilbert spaces and give some of their properties. This will lead us to the semigroups and to the Hille-Yosida's Theorem. If we have enough time, we will see several applications.