We bring together the theories of duality and dynamic programming. We show that the dual of a separable dynamic optimization problem can be recursively decomposed. We provide a dual version of the principle of optimality and give conditions under which the dual Bellman operator is a contraction...

In this paper a simple dynamic optimization problem is solved with the help of the recursive saddle point method developed by Marcet and Marimon (1999). According to Marcet and Marimon, their technique should yield a full characterization of the set of solutions for this problem. We show though,...

We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal...

Several recent papers have proposed recursive Lagrangian-based methods for solving dynamic contracting problems. These methods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual...

Many dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual...

Several recent papers have proposed recursive Lagrangian-basedmethods for solving dynamic contracting problems. Thesemethods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual...

We also explore the robustness of our model when second period valuations are correlated across individuals, and when each individual's first and second period types are correlated.