Longevity risk (LR) is undoubtedly a much discussed actuarial subject at international level; it implicates uncertainty of mortality rates in the long term (i.e., unanticipated inter-temporal variations) and the consequent effects on long term survival probabilities. Public and private annuities providers (as pension funds and insurance companies) are involved in hedging the LR; a classical decision procedure can be structured to solve an asset-liability mismatching problem, introducing financial tools with payoff linked to longevity or mortality indexes.