Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

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Peer-to-peer (P2P) insurance promises lower costs and better alignment of interests by having small groups of policyholders directly share risk. Yet full pooling can destroy prevention incentives under moral hazard, while self-insurance sacrifices diversification. In this talk, we develop a unified mean–variance framework that endogenizes both the pooling matrix and the effort levels in one joint optimization.

Zajíček's theorem characterizes the sets of non-differentiability of convex functions.
Its statement is sharp, elegant and tremendously powerful.
We provide the proof in a simple case and give some applications.

Based on the mechanical viewpoint that living tissues present a fluid-like behaviour, Partial Differential Equations models inspired by fluid dynamics are nowadays well established as one of the main mathematical tools for the macroscopic description of tissue growth. Depending on the type of tissue, these models link the pressure to the velocity field using either Brinkman’s law (visco-elastic models) or Darcy’s law (porous-medium equations (PME)).

A cellular automaton is monotonous if it preserves the order on configurations inherited from an order on

states. If at first sight, the significantly sparse aspect of that product order lead us to believe that mono-

tonicity would not be that restrictive, the fact that cellular automata are characterised by a local rule

applied shift-invariantly makes the impact of this constraint more remarkable than expected. After intro-

ducing the basic concepts of our work, we first state general results about monotonous cellular automata