The conjoint effects of stochastic risks on insurance portfolio internal models

The study analyses the interplay between specific market consistent assumptions for interest rates, based on stochastic simulation procedures, and a dynamic demographic description. In particular, in the context of the Lee Carter survival model, in order to get more reliable and accurate mortality projections, we propose the semi parametric bootstrap based on the Poisson distribution: the Stratified Sampling Bootstrap, reducing the variance estimator by means of Variance Reducing Techniques (VRT’s). The framework, in which the question is deepened and then applied, is the complex financial system of the pension annuity portfolio. In this context interest rates future evolution interacts with the uncertainty in future lifetimes, in particularly due to the systematic effects of the longevity phenomenon. Internal models have to be used for management and Solvency Capital Requirement purposes and the “right” description of the future financial and demographic scenario constitutes a great issue. In the paper we propose closed formulas for the portfolio surplus calculation in stochastic hypotheses for the main risk drivers.