Some remarks on continuos annuities in a stochastic interest and mortality scenario.

The paper deals with the decomposition of opportune tools in order to value continuos annuities in an enviroment in which both future rates of returns and mortality are stochastic. By means of stochastic instruments involving the discounting process, in the first part of the paper, the first two moments of the present value of a continuos life annuity are calculated and, generalizing traditional techniques, the riskiness connected to it is estimeted. On the other side aim of the paper is to take into account also the evolution of mortality and its consequences in valuation of annuities. Therefore, in the second part of the paper a portfolio of continuos annuities under deterministic assumptions about the rates of return is considered, and also by means of numerical exemples, the influence of mortality projections on portfolio valuations is shown. The analysis takes into account the measure of the risk deriving from different projections.