FFT, Extreme Value Theory and Simulation to model non life insurance claims dependences

This paper shows an example of integrated use of three different approacheslike Extreme Value Theory (EVT), two-dimensional Fast Fourier Transform(FFT) and Monte Carlo simulation to model non life insurance company aggregatelosses, taking into account the need of Internal Risk Models development in the lightof Solvency II European project. In particular EVT permits to define the truncationpoint between small and large claims. Two-dimensional FFT is used to model notonly aggregate losses, but dependence between its basic components too. FinallyMonte Carlo simulation describes large claims behaviour. Collective Risk Model hasbeen developed using Matlab software.