  In this paper we develop a general framework to analyze stochastic dynamic
problems with unbounded utility functions and correlated and unbounded shocks.
We obtain new results of the existence and uniqueness of solutions to the
Bellman equation through a general fixed point theorem that generalizes known
results for Banach contractions and local contractions. We study an endogenous
growth model as well as the Lucas asset pricing model in an exchange economy,
significantly expanding their range of applicability.
