Solvency Capital Requirements for Longevity Risk under different stochastic mortality models

The work aims to quantify the risk associated with the estimation of future mortality on a port- folio of immediate life annuities. Particular attention is devoted to the longevity risk generated from the stochastic nature of mortality and to the model and parameters choice. In order to control for the model risk inherent in the forecasts, we apply three different and well-known stochastic mortality models: the Kannisto model, the Linear Decline model, and the Lee-Carter model. For each model, with the aid of the bootstrap technique we control for the parameter risk. Forecasts are necessary for decision making: the recognition of different sources of uncertainty is the starting point for the calculation of the solvency capital requirements in Solvency II project. We present the criteria that define those capitals for an (re)insurance company, with a particular focus on longevity risk.