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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...
Persistent link: https://www.econbiz.de/10011188029
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,...
Persistent link: https://www.econbiz.de/10005041887
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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...
Persistent link: https://www.econbiz.de/10010539721
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...
Persistent link: https://www.econbiz.de/10010555597
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...
Persistent link: https://www.econbiz.de/10010570164
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...
Persistent link: https://www.econbiz.de/10009350243
Many separable 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...
Persistent link: https://www.econbiz.de/10008864035