IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation

  • Cuong Le Van

    (University of Paris 1, CNRS, Centre d’ Economie de la Sorbonne, Paris School of Economics)

  • Lisa Morhaim

    (University of Paris 1, CNRS, Centre d’ Economie de la Sorbonne, Paris School of Economics, Institute Math´ematique de Bourgogne)

  • Yiannis Vailakis

    (Department of Economics, University of Exeter)

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://people.exeter.ac.uk/cc371/RePEc/dpapers/DP0803.pdf
Download Restriction: no

Paper provided by Exeter University, Department of Economics in its series Discussion Papers with number 0803.

as
in new window

Length:
Date of creation: 2008
Date of revision:
Handle: RePEc:exe:wpaper:0803
Contact details of provider: Postal:
Streatham Court, Rennes Drive, Exeter EX4 4PU

Phone: (01392) 263218
Fax: (01392) 263242
Web page: http://business-school.exeter.ac.uk/about/departments/economics/

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
  2. Peter A. Streufert, 1990. "Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 79-97.
  3. Olivier F. Morand & Kevin L. Reffett, 2002. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Tinbergen Institute Discussion Papers 02-085/2, Tinbergen Institute.
  4. LE VAN, Cuong & VAILAKIS, Yiannis, 2002. "Recursive utility and optimal growth with bounded or unbounded returns," CORE Discussion Papers 2002055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Coleman, Wilbur II, 2000. "Uniqueness of an Equilibrium in Infinite-Horizon Economies Subject to Taxes and Externalities," Journal of Economic Theory, Elsevier, vol. 95(1), pages 71-78, November.
  6. Kennan,J., 2001. "Uniqueness of positive fixed points for increasing concave functions on Rn : an elementary result," Working papers 2, Wisconsin Madison - Social Systems.
  7. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
  8. Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Annals of Operations Research, Springer, vol. 114(1), pages 117-144, August.
  9. Duran, Jorge, 1997. "On dynamic programming with unbounded returns," CEPREMAP Working Papers (Couverture Orange) 9710, CEPREMAP.
  10. Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, 09.
  11. Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:exe:wpaper:0803. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Carlos Cortinhas)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.