Internal risk control by solvency measures

The paper deals with the solvency analysis through internal models in the case of a portfolio of life annuities, focusing on the interplay between stochastic interest rate dynamics and the survival evolution in time. This specific aspect is investigated basing the survival death rates on Poisson Lee Carter model approached according to the Iterative Procedure and two simulated approaches on the Poisson Lee Carter: the Standard Procedure and the Stratified Sampling Procedure. The financial aspect, particularly notable in portfolios with long duration and multiplicity of payments as in the considered case, is tackled assuming different stochastic hypotheses on the interest rates evolution. Aim of the paper is to deepen the reaction of solvency measures as the surplus index and the ruin probability to the specific financial and demographic scenario. The indexes are studied in different loading factor assumptions and several numerical applications illustrate the model setup.