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

  • Grochulski, Borys
  • Zhang, Yuzhe

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agentʼs consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agentʼs income realized to date. We characterize this function in terms of the agentʼs outside option value function and the discounted amount of time in which the agentʼs 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.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 6 ()
Pages: 2356-2388

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:6:p:2356-2388
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. 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.
  2. Krueger, Dirk & Uhlig, Harald, 2005. "Competitive risk sharing contracts with one-sided commitment," CFS Working Paper Series 2005/07, Center for Financial Studies (CFS).
  3. Milton Harris & Bengt Holmstrom, 1981. "A Theory of Wage Dynamics," Discussion Papers 488, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Patrick J. Kehoe & Fabrizio Perri, 2003. "Competitive equilibria with limited enforcement," Staff Report 307, Federal Reserve Bank of Minneapolis.
  5. Zhang, Yuzhe, 2009. "Dynamic Contracting with Persistent Shocks," MPRA Paper 23108, University Library of Munich, Germany.
  6. Kehoe, Timothy J & Levine, David K, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 865-88, October.
  7. 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.
  8. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, June.
  9. Stefania Albanesi & Christopher Sleet, 2006. "Dynamic Optimal Taxation with Private Information," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 1-30.
  10. 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.
  11. Alexander Monge-Naranjo, 2009. "Entrepreneurship and firm heterogeneity with limited enforcement," Annals of Finance, Springer, vol. 5(3), pages 465-494, June.
  12. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2002. "Optimal Indirect and Capital Taxation," Levine's Working Paper Archive 391749000000000449, David K. Levine.
  13. Tomasz Piskorski & Alexei Tchistyi, 2010. "Optimal Mortgage Design," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3098-3140, August.
  14. 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.
  15. Rui Albuquerque & Hugo Hopenhayn, 2002. "Optimal Lending Contracts and Firm Dynamics," RCER Working Papers 493, University of Rochester - Center for Economic Research (RCER).
  16. Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean-Charles, 2004. "Dynamic Security Design," CEPR Discussion Papers 4753, C.E.P.R. Discussion Papers.
  17. Albert Marcet & Ramon Marimon, 1992. "Communication, commitment, and growth," Discussion Paper / Institute for Empirical Macroeconomics 74, Federal Reserve Bank of Minneapolis.
  18. 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.
  19. Thomas, Jonathan & Worrall, Tim, 1988. "Self-enforcing Wage Contracts," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 541-54, October.
  20. 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.
  21. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
  22. 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.
  23. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
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