The economic model of insurance is based on mutualization. Roughly speaking, this consists in considering that the good results of the majority of the insureds compensate for the losses linked to the claims of a minority. Mathematically, it is based on the law of large numbers and the central limit theorem. But new risks, on a large scale, such as cyber, climatic or epidemiological risks, can challenge this model. On the one hand, the scale of the associated disasters, which takes us away from the hypotheses of the central limit theorem, and on the other hand, the statistical ignorance of the phenomena considered, which makes their anticipation and coverage complicated. The question of the (mathematical) insurability of these risks is clearly raised.
The objective of this course is to understand and master the mathematical and statistical tools necessary for the analysis of extreme risks. We will present the main mathematical issues related to the study of these extreme risks and show how mathematical modeling and the relevant use of the (often scarce) data available can be used to build management solutions for this type of risk.