IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

  • Grochulskiy, Borys
  • Zhang, Yuzhe

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent's consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent's income realized to date. We characterize this function in terms of the agent's outside option value function and the discounted amount of time in which the agent's income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez-Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley-Aiyagari incomplete-markets models.

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://mpra.ub.uni-muenchen.de/36539/1/MPRA_paper_36539.pdf
File Function: original version
Download Restriction: no

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36539.

as
in new window

Length:
Date of creation: 22 Jul 2011
Date of revision:
Handle: RePEc:pra:mprapa:36539
Contact details of provider: Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de

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. Kehoe, Timothy J & Levine, David K, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 865-88, October.
  2. Zhang, Yuzhe, 2012. "Characterization of a Risk Sharing Contract with One-Sided Commitment," MPRA Paper 42820, University Library of Munich, Germany, revised Aug 2012.
  3. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 957-984.
  4. Tomasz Piskorski & Alexei Tchistyi, 2010. "Optimal Mortgage Design," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3098-3140, August.
  5. Thomas, Jonathan & Worrall, Tim, 1988. "Self-enforcing Wage Contracts," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 541-54, October.
  6. Mikhail Golosov & Narayana R. Kocherlakota & Aleh Tsyvinski, 2001. "Optimal indirect and capital taxation," Working Papers 615, Federal Reserve Bank of Minneapolis.
  7. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
  8. Stefania Albanesi & Christopher Sleet, 2004. "Dynamic optimal taxation with private information," Discussion Paper / Institute for Empirical Macroeconomics 140, Federal Reserve Bank of Minneapolis.
  9. Krueger, Dirk & Uhlig, Harald, 2004. "Competitive Risk Sharing Contracts with One-Sided Commitment," CEPR Discussion Papers 4208, C.E.P.R. Discussion Papers.
  10. Milton Harris & Bengt Holmstrom, 1981. "A Theory of Wage Dynamics," Discussion Papers 488, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 345-390.
  12. Dirk Krueger & Fabrizio Perri, 2006. "Does Income Inequality Lead to Consumption Inequality? Evidence and Theory -super-1," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 163-193.
  13. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
  14. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, vol. 68(4), pages 775-798, July.
  15. Guillaume Plantin & Bruno Biais & Thomas Mariotti & Jean-Charles Rochet, 2004. "Dynamic Security Design," GSIA Working Papers 2005-E5, Carnegie Mellon University, Tepper School of Business.
  16. Alexander Monge-Naranjo, 2009. "Entrepreneurship and firm heterogeneity with limited enforcement," Annals of Finance, Springer, vol. 5(3), pages 465-494, June.
  17. Albert Marcet & Ramon Marimon, 1992. "Communication, commitment, and growth," Discussion Paper / Institute for Empirical Macroeconomics 74, Federal Reserve Bank of Minneapolis.
  18. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, June.
  19. Patrick J. Kehoe & Fabrizio Perri, 2002. "Competitive equilibria with limited enforcement," Working Papers 621, Federal Reserve Bank of Minneapolis.
  20. Rui Albuquerque & Hugo A. Hopenhayn, 2004. "Optimal Lending Contracts and Firm Dynamics," Review of Economic Studies, Wiley Blackwell, vol. 71(2), pages 285-315, 04.
  21. Zhiguo He, 2009. "Optimal Executive Compensation when Firm Size Follows Geometric Brownian Motion," Review of Financial Studies, Society for Financial Studies, vol. 22(2), pages 859-892, February.
  22. Kocherlakota, Narayana R, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 595-609, October.
  23. Eaton, Jonathan & Gersovitz, Mark, 1981. "Debt with Potential Repudiation: Theoretical and Empirical Analysis," Review of Economic Studies, Wiley Blackwell, vol. 48(2), pages 289-309, 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:pra:mprapa:36539. 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: (Ekkehart Schlicht)

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.