Aggregazione dei rischi di sottoscrizione per l'assicurazione danni: metodi di stima per la correlazione tra rischi di tariffazione e riservazione

The introduction of Solvency II regulatory framework enhanced a new risk-based capital evaluation, which can be seen as a powerful opportunity for the undertakings to better manage their capitals. Under the new risk-based regulation, the support of quantitative considerations should allow companies to estimate a capital requirement that better reflects their own risk profile, without under- or over-estimations that could lead to a lack of efficiency in the capital structure. The purpose of this thesis is to define the concept of risk aggregation, as far as Non-Life Underwriting risk is concerned. First, we introduce the Solvency II directive and its pillar structure, with a legal and juridical overview of the approval process of (Partial) Internal Models described in the Directive. Afterwards, the Solvency Capital Requirement calculation procedure is explained and the most relevant risk module for a Non-Life insurance company, i.e. Premium and Reserve Risk, is introduced. After this introduction, we describe the correlation structure within the Standard Formula and compare the correlation provided by EIOPA with alternatives obtained using different divers. In order to provide a practical example of the alternative correlation estimation approaches, we have implemented some of the methodologies previously described and compared the SCR obtained with the Standard Formula with the SCR obtained with these procedures. Moreover, we provide some sensitivity analysis in order to further inspect the impact of changes in the correlation structure during extreme events. Furthermore, alternatives to risk aggregation through linear correlation, i.e. the Copula function, are given. Indeed, risk aggregation through copulas allows to overcome the limitations and weaknesses of the first approach. Finally, a practical example of the Expert Judgement process adopted to adjust the correlation between risks. The aim of this process is to allow the correlation structure to reflect both quantitative and qualitative considerations coming from business experts, which otherwise would be neglected.