The aim of this work is to provide a strategy to face up with the longevity risk with specific regard to life annuities. Specifically, this work follows the model introduced in [1], where an appropriate scheme of life annuity is designed so that the longevity risk could be immunized by means of a financial compensation. In this scheme, benefits are dynamically linked to the actual and observed trends in either investment rates and mortality rates, and the concept of financial and demographic revaluation is introduced. Differently from other approaches later introduced in literature with the aim of sharing the longevity risk between annuity provider and policyholders, the model described in this work is proved to be effective and efficient for the longevity risk managing as at every recurrence of the contract the annuity provider is able to face with its commitments and has exactly the reserve necessary to cover liabilities towards the annuitants who are still alive. A numerical section is provided to illustrate both the model and its efficiency.