Recursive contracts

Abstract

We obtain a recursive formulation for a general class of contracting problems involving incentive constraints. These constraints make the corresponding maximization (sup) problems non recursive. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle point (infsup) functional equation (analogous to Bellman's equation) that characterizes the solution. Our approach applies to a large class of contractual problems, as examples, we study the optimal policies in a model intertemporal participation (default) constraints and a model with competitive constraints (as in Ramsey problems).