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

Existence and Uniqueness of Solutions to the Stochastic Bellman Equation with Unbounded Shock