Requisito di capitale e correlazione tra i rami:i risultati di un modello interno

[Autom. eng. transl.] The process of revising the entire solvency structure, called Solvency II, was directed towards the well-known three-pillar model. In particular, the need to ensure that companies have an appropriate capital at risk and to encourage insurers to develop and use better risk management techniques, provide the starting point for the development of appropriate internal models. In this article we will proceed to the construction of an internal model, based on a classical risk theory relationship, appropriately extended in order to consider the correlations between the branches. In particular, the dependencies between the number and the costs of the claims will be modeled using different copula functions and the model will be applied in order to assess the necessary requirement for the premium risk, for a hypothetical company with two lines of business. In the final part the results obtained will be compared with the International Actuarial Association approach and with the Solvency Capital Requirement proposed by the recent quantitative study of CEIOPS (QIS3). This comparison will allow both to verify the efficiency of the model with respect to the application of two standard formulas, and to compare the use of copulas with alternative correlation modeling methods.