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This paper was prepared for the First Journées d'Economie et Econométrie de l'Asssurance, in Rennes, October 22nd and 23rd, 2009. It's a melting pot of several papers that I have written with my co-authors, plus a very short summary of Graciella Chichilnisky enlightening results. But, before proposing partial answers to the problem of modelling catastrophes in such a way as to be able to propose how to manage them, I try and grasp what we mean by catastrophe and what are the main problems, in the introduction.