The demographic risk assessment: from the traditional Local GAAP framework to the Solvency II market-consistent one

The purpose of this thesis is to provide a stochastic model consistent with the accounting principles envisaged by Directive 138/2009/EC aimed at quantifying demographic risk. This model, already developed in a local accounting context, is then adapted to market-consistent valuation, highlighting the bridge between the two frameworks, the individual risks that are quantified and the differences in terms of numerical results. The application of the model leads to the identification of some sub-risks inherent to the demographic one: the idiosyncratic, the trend one and a risk linked to risk-free rate changes. For the first risk, using an approach based on the concept of cohorts, closed formula results are obtained about expected value, standard deviation and skewness. Moreover, it is possible to numerically quantify the capital requirement and, at the same time, approximate it according to the characteristics of the profit (loss) random variable. Regarding the second risk, the model pursues the aim of quantifying the Solvency Capital Requirement by simulating the possible trajectories of mortality and obtaining the simulated distribution of the company's profit (loss) linked to the possible variation in demographic expectations. Thus, it was possible to numerically quantify the capital requirement coherently with in force regulatory principles.