Recursive contracts

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).