Savings operations over random periods

Due to the ageing of the population, public pension plans are increasingly being implemented by private savings schemes. This therefore gives rise to a wide range of innovative schemes to meet the varying needs of savers and financial institutions. Therefore, the aim of this paper is to propose a savings operation which includes the randomness derived from the contingency which supposes the eventual but unpredictable death of the saver. We have developed this type of operation by applying a financial-actuarial methodology and thereby deducing a way of calculating all amounts resulting from the savings operation, and introducing a new quantity derived from this randomness, namely the risk quota. Similarly, we have indicated how to calculate different measures of (gross and net) profitability, in random terms and the part corresponding to this randomness.