Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case

Juan Pablo RincÛn-Zapatero and Carlos RodrÌguez-Palmero
Authors registered in the RePEc Author Service: Juan Pablo Rincón-Zapatero

Econometrica, 2003, vol. 71, issue 5, 1519-1555

Abstract: We study the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns. We introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space, and on the application of some metric fixed point theorems. With appropriate conditions we prove uniqueness of solutions with respect to the whole space of continuous functions. Furthermore, the paper provides new sufficient conditions for the existence of solutions that can be applied to fairly general models. It is also proven that the fixed point coincides with the value function and that it can be approached by successive iterations of the Bellman operator. Copyright The Econometric Society 2003.

Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (36)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ecm:emetrp:v:71:y:2003:i:5:p:1519-1555

Ordering information: This journal article can be ordered from
https://www.economet ... ordering-back-issues

Access Statistics for this article

Econometrica is currently edited by Guido Imbens

More articles in Econometrica from Econometric Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().