Yiannis Vailakis

Existence and Uniqueness of a Fixed Point for Local Contractions

This paper proves the existence and uniqueness of a fixed point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point result can apply to study the existence and uniqueness of solutions to some recursive equations that arise in economic dynamics. Copyright 2010 The Econometric Society.

Convex dynamic programming with (bounded) recursive utility

We consider convex dynamic programs with general (bounded) recursive utilities. The Contraction Mapping Theorem fails when the utility aggregator does not obey any discounting property. This failure occurs even with traditional aggregators and certainty equivalent specifications. However, the Bellman operator admits a unique fixed point when an interior policy is feasible. This happens because utility values are unique at interior consumption plans and, when an interior perturbation is feasible, drops in utility values can be avoided.

Sovereign debt and incentives to default with uninsurable risks

We show that sovereign debt is unsustainable if debt contracts are not supported by direct sanctions and default carries only a ban from ever borrowing in financial markets even in the presence of uninsurable risks and time-varying interest rate. This extension of Bulow and Rogoff (1989) requires that the present value of the endowment be finite under the most optimistic valuation. We provide examples where this condition fails and sovereign debt is sustained by the threat of loss of insurance opportunities upon default, despite the fact that the most pessimistic valuation of the endowment, the natural debt limit, is finite.