Capital Requirements for aggregate risks in longterm living products: a stochastic approach

Referring to the Solvency II regulation, aim of the paper is to obtain an estimate for the Solvency Capital Requirement of a life annuity portfolio when stochastic interest and mortality rates are considered. We propose a computationally tractable approach that yields an estimate for the required solvency capital when mortality and interest rates are forecasted by means of diffusion processes. To this end we determine the capital requirements for each considered risk factor and then we compute the Global Solvency Capital Requirement. Numerical applications analyzing the effect of the choice of different scenarios on the Global SCR quantification are proposed