IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/36539.html
   My bibliography  Save this paper

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

Author

Listed:
  • Grochulskiy, Borys
  • Zhang, Yuzhe

Abstract

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.

Suggested Citation

  • Grochulskiy, Borys & Zhang, Yuzhe, 2011. "Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment," MPRA Paper 36539, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:36539
    as

    Download full text from publisher

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rui Albuquerque & Hugo A. Hopenhayn, 2004. "Optimal Lending Contracts and Firm Dynamics," Review of Economic Studies, Oxford University Press, vol. 71(2), pages 285-315.
    2. Zhang, Yuzhe, 2013. "Characterization of a risk sharing contract with one-sided commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 794-809.
    3. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    4. Krueger, Dirk & Uhlig, Harald, 2006. "Competitive risk sharing contracts with one-sided commitment," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1661-1691, October.
    5. 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.
    6. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, September.
    7. Marcet, Albert & Marimon, Ramon, 1992. "Communication, commitment, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 219-249, December.
    8. Stefania Albanesi & Christopher Sleet, 2006. "Dynamic Optimal Taxation with Private Information," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 1-30.
    9. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2003. "Optimal Indirect and Capital Taxation," Review of Economic Studies, Oxford University Press, vol. 70(3), pages 569-587.
    10. 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.
    11. Kehoe, Patrick J. & Perri, Fabrizio, 2004. "Competitive equilibria with limited enforcement," Journal of Economic Theory, Elsevier, vol. 119(1), pages 184-206, November.
    12. Timothy J. Kehoe & David K. Levine, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 865-888.
    13. Jonathan Eaton & Mark Gersovitz, 1981. "Debt with Potential Repudiation: Theoretical and Empirical Analysis," Review of Economic Studies, Oxford University Press, vol. 48(2), pages 289-309.
    14. 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.
    15. Milton Harris & Bengt Holmstrom, 1982. "A Theory of Wage Dynamics," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 315-333.
    16. Jonathan Thomas & Tim Worrall, 1988. "Self-Enforcing Wage Contracts," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 541-554.
    17. 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.
    18. 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.
    19. Tomasz Piskorski & Alexei Tchistyi, 2010. "Optimal Mortgage Design," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3098-3140, August.
    20. 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.
    21. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    22. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Oxford University Press, vol. 63(4), pages 595-609.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Bo & Niu, Yingjie & Zhang, Yuhua, 2019. "Corporate liquidity and risk management with time-inconsistent preferences," Economic Modelling, Elsevier, vol. 81(C), pages 295-307.
    2. Daniel Bird & Alexander Frug, 2019. "Monotone contracts," Economics Working Papers 1647, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Patrick Bolton & Neng Wang & Jinqiang Yang, 2019. "Optimal Contracting, Corporate Finance, and Valuation with Inalienable Human Capital," Journal of Finance, American Finance Association, vol. 74(3), pages 1363-1429, June.
    4. Rui Li & Dana Kiku & Hengjie Ai, 2014. "A Mechanism Design Model of Firm Dynamics: The Case of Limited Commitment," 2014 Meeting Papers 855, Society for Economic Dynamics.
    5. Borys Grochulski & Yuzhe Zhang, 2017. "Market‐Based Incentives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58, pages 331-382, May.
    6. Zhang, Yuzhe, 2013. "Characterization of a risk sharing contract with one-sided commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 794-809.
    7. Wang, Cheng & Yang, Youzhi, 2019. "Optimal self-enforcement and termination," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 161-186.
    8. Jeon, Junkee & Koo, Hyeng Keun & Shin, Yong Hyun, 2018. "Portfolio selection with consumption ratcheting," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 153-182.
    9. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    10. Yaping Shan, 2013. "Incentives for Research Agents: Optimal Contracts and Implementation," School of Economics Working Papers 2013-20, University of Adelaide, School of Economics.
    11. Patrick Bolton & Neng Wang & Jinqiang Yang, 2019. "Optimal Contracting, Corporate Finance, and Valuation with Inalienable Human Capital," Journal of Finance, American Finance Association, vol. 74(3), pages 1363-1429, June.
    12. Yaping Shan, 2017. "Optimal contracts for research agents," RAND Journal of Economics, RAND Corporation, vol. 48(1), pages 94-124, March.
    13. Yaping Shan, 2017. "Incentives for Research Agents and Performance-vested Equity-based Compensation," School of Economics Working Papers 2017-15, University of Adelaide, School of Economics.
    14. Niu, Yingjie & Yang, Jinqiang & Zou, Zhentao, 2020. "Robust contracts with one-sided commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    15. Junkee Jeon & Hyeng Keun Koo & Kyunghyun Park, 2018. "Optimal Insurance with Limited Commitment in a Finite Horizon," Papers 1812.11669, arXiv.org, revised Jan 2019.
    16. Ai, Hengjie & Li, Rui, 2015. "Investment and CEO compensation under limited commitment," Journal of Financial Economics, Elsevier, vol. 116(3), pages 452-472.
    17. Felix Feng, 2018. "Dynamic Compensation under Uncertainty Shocks and Limited Commitment," 2018 Meeting Papers 159, Society for Economic Dynamics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    2. Grochulski, Borys & Zhang, Yuzhe, 2009. "Borrowing Constraint as an Optimal Contract," MPRA Paper 23216, University Library of Munich, Germany.
    3. Patrick Bolton & Neng Wang & Jinqiang Yang, 2019. "Optimal Contracting, Corporate Finance, and Valuation with Inalienable Human Capital," Journal of Finance, American Finance Association, vol. 74(3), pages 1363-1429, June.
    4. Patrick Bolton & Neng Wang & Jinqiang Yang, 2016. "Liquidity and Risk Management: Coordinating Investment and Compensation Policies," 2016 Meeting Papers 1703, Society for Economic Dynamics.
    5. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    6. Alvaro Aguirre, 2017. "Contracting Institutions and Economic Growth," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 24, pages 192-217, March.
    7. Yili Chien & Junsang Lee, 2006. "Why Tax Capital?," 2006 Meeting Papers 492, Society for Economic Dynamics.
    8. Karaivanov, Alexander K. & Martin, Fernando M., 2018. "Markov-perfect risk sharing, moral hazard and limited commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 1-23.
    9. Árpád Ábrahám & Sarolta Laczó, 2018. "Efficient Risk Sharing with Limited Commitment and Storage," Review of Economic Studies, Oxford University Press, vol. 85(3), pages 1389-1424.
    10. YiLi Chien & JunSang Lee, 2006. "Optimal Capital Taxation under Limited Commitment," 2006 Meeting Papers 430, Society for Economic Dynamics.
    11. Zhang, Yuzhe, 2013. "Characterization of a risk sharing contract with one-sided commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 794-809.
    12. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2013. "Fragility of Competitive Equilibrium with Risk of Default," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(2), pages 271-295, April.
    13. Almuth Scholl, 2002. "Limited Enforceable International Loans, International Risk Sharing and Trade," SFB 649 Discussion Papers SFB649DP2005-055, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2005.
    14. Bauducco, Sofia & Caprioli, Francesco, 2014. "Optimal fiscal policy in a small open economy with limited commitment," Journal of International Economics, Elsevier, vol. 93(2), pages 302-315.
    15. Christian Hellwig & Guido Lorenzoni, 2009. "Bubbles and Self-Enforcing Debt," Econometrica, Econometric Society, vol. 77(4), pages 1137-1164, July.
    16. Edmans, Alex & Gabaix, Xavier & Sadzik, Tomasz & Sannikov, Yuliy, 2009. "Dynamic Incentive Accounts," CEPR Discussion Papers 7497, C.E.P.R. Discussion Papers.
    17. Tom Krebs & Moritz Kuhn & Mark Wright, 2017. "Under-Insurance in Human Capital Models with Limited Enforcement," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 25, pages 121-150, April.
    18. Ai, Hengjie & Li, Rui, 2015. "Investment and CEO compensation under limited commitment," Journal of Financial Economics, Elsevier, vol. 116(3), pages 452-472.
    19. Sergio Rebelo & Neng Wang & Jinqiang Yang, 2018. "Rare Disasters, Financial Development, and Sovereign Debt," NBER Working Papers 25031, National Bureau of Economic Research, Inc.
    20. Dirk Krueger, 2006. "Public Insurance against Idiosyncratic and Aggregate Risk: The Case of Social Security and Progressive Income Taxation," CESifo Economic Studies, CESifo, vol. 52(4), pages 587-620, December.

    More about this item

    Keywords

    Limited commitment; Borrowing constraints;

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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: (Joachim Winter). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.