  This paper provides new conditions for dynamic optimality in discrete time
and uses them to establish fundamental dynamic programming results for several
commonly used recursive preference specifications. These include Epstein-Zin
preferences, risk-sensitive preferences, narrow framing models and recursive
preferences with sensitivity to ambiguity. The results obtained for these
applications include (i) existence of optimal policies, (ii) uniqueness of
solutions to the Bellman equation, (iii) a complete characterization of optimal
policies via Bellman's principle of optimality, and (iv) a globally convergent
method of computation via value function iteration.
