Estimate Some Tools Probabilistic in Insurance and Finance

Abstract

: Extreme Value Theory (EVT) originated, in 1928, in the work of Fisher and Tippett describing the behavior of the maximum of independent and identically distributed random variables. Various applications have been implemented successfully in many fields such as: actuarial science, finance, economics, hydrology, climatology, telecommunications and engineering sciences. In this thesis, we give an overview on the extreme value theory and the different methods of estimation of the tail index and the extreme quintiles. This thesis contains two applications of the extreme value theory, in particularly when the extreme value index is positive, which corresponds to the class of heavy-tailed distributions frequently used to model real data sets. The first is an application in the actuarial domain, to estimate one of the most popular risk measures, called the conditional tail expectation (CTE). The second contribution is an important application in fields of industrial reliability, warranty systems and telecommunications, to approximate the renewal function.