In this paper we develop a framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results about the existence and uniqueness of solutions to the Bellman equation through a notion of Banach contractions that generalizes known results for Banach and local...

The paper provides a systematic way for finding a partial differential equation that characterize directly the optimal control, in the framework of one?dimensional stochastic control problems of Mayer, with no constraints on the controls. The results obtained are applied to some significative...

This paper gives a new method to characterize Markov Perfect Nash Equilibrium in stochastic differential games by means of a set of Generalized Euler Equations. Necessary and sufficient conditions are given.