The estimation of the actuarial reserves is a pivotal point for the finances of a firm with pension liabilities. In this article a strategy is proposed for the estimation of the actuarial reserve of a life annuity (for one life period), considering an stochastic dynamic integrated with a hedging strategy that guarantees a future value of the reserve greater or equal than the payment due. The theoretical approach is relevant in so far as it allows to diminish the cost of the life annuity, with the social and fiscal benefits that it would entail, by allowing the retirement systems to have greater coverage