Perte d’exploitation, une application de la théorie des extrêmes

Je remets ici un lien vers un vieux papier puisque plusieurs personnes m’en ont récemment demandé une version électronique. La version officielle du papier est en ligne sur le site du Bulletin Français d’Actuariat (http://www.institutdesactuaires.com/bfa/, ou ici pour le papier tel qu’il a été publié). Pour ceux qui souhaitent aller plus loin, je mets à leur disposition la base (brute, xls) qui a servie à l’étude. Il s’agit de la version expurgée des noms des assurés, ainsi que de (certaines) informations sur les contrats.

Insurability is a major issue for risk managers in the insurance industry. Zajdenweber (1996) mentioned that business interruption is hardly insurable, using extreme value results: the right tail of the distribution should be modeled using some Pareto distribution with parameter 1, which has none finite moment. Since the expected value in tails is infinite, on a theoretical point of view, it becomes impossible to assess the price of that risk, and to hedge it using standard insurance covers. As we shall see, the use of more advanced results in extreme value theory (a wide survey will be proposed) may let us think that the assumption of very fat tails may be not relevant. For instance, we will propose a test to see if a distribution has a finite mean. We shall also discuss at the end the use of the pure premium as a criteria to assess whether a risk is or not insurable.


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