The authors develop the classical asset pricing analysis assuming that the representative agent of a Lucas's equilibrium model is characterized by an instantaneous utility which is as usual a function of the consumption but which is also affected negatively by a process describing the agent's aspiration. This aspiration is given by a linear combination of the current habit (forward term) and of the conditional expectation of the habit at the end of the agent's life (backward term). Using the forward-backward SDE's theory, the authors solve the optimal consumption problem and compute the Arrow-Debreu price process, the interest rate at equilibrium and the asset risk premium assuming that the endowment process belongs to the Itô processes class and using Malliavin calculus techniques.