We obtain a recursive formulation for a general class of contracting
problems involving incentive constraints. Under these constraints,
the corresponding maximization (sup) problems fails to have a
recursive solution. Our approach consists of studying the Lagrangian.
We show that, under standard assumptions, the solution to the
Lagrangian is characterized by a recursive saddle point (infsup)
functional equation, analogous to Bellman's equation. Our approach
applies to a large class of contractual ...
We obtain a recursive formulation for a general class of contracting
problems involving incentive constraints. Under these constraints,
the corresponding maximization (sup) problems fails to have a
recursive solution. Our approach consists of studying the Lagrangian.
We show that, under standard assumptions, the solution to the
Lagrangian is characterized by a recursive saddle point (infsup)
functional equation, analogous to Bellman's equation. Our approach
applies to a large class of contractual problems. As examples, we
study the optimal policy in a model with intertemporal participation
constraints (which arise in models of default) and intertemporal
competitive constraints (which arise in Ramsey equilibria).
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