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

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  • 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.

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  • 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
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    Cited by:

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    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. 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.
    6. Hengjie Ai & Dana Kiku & Rui Li & Jincheng Tong, 2021. "A Unified Model of Firm Dynamics with Limited Commitment and Assortative Matching," Journal of Finance, American Finance Association, vol. 76(1), pages 317-356, February.
    7. 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.
    8. Yaping Shan, 2013. "Incentives for Research Agents: Optimal Contracts and Implementation," School of Economics and Public Policy Working Papers 2013-20, University of Adelaide, School of Economics and Public Policy.
    9. Yaping Shan, 2017. "Optimal contracts for research agents," RAND Journal of Economics, RAND Corporation, vol. 48(1), pages 94-124, March.
    10. Krueger, Dirk & Uhlig, Harald, 2022. "Neoclassical Growth with Long-Term One-Sided Commitment Contracts," CEPR Discussion Papers 17757, C.E.P.R. Discussion Papers.
    11. Th'eo Durandard, 2023. "Dynamic delegation in promotion contests," Papers 2308.05668, arXiv.org.
    12. Niu, Yingjie & Yang, Jinqiang & Zou, Zhentao, 2020. "Robust contracts with one-sided commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    13. 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(2), pages 331-382, May.
    14. Felix Feng, 2018. "Dynamic Compensation under Uncertainty Shocks and Limited Commitment," 2018 Meeting Papers 159, Society for Economic Dynamics.
    15. Shan, Yaping, 2019. "Incentives for research agents and performance-vested equity-based compensation," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 44-69.
    16. Wang, Cheng & Yang, Youzhi, 2019. "Optimal self-enforcement and termination," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 161-186.
    17. 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.
    18. Ma, Jinrun & Wu, Yaoyao & Liang, Yongtang, 2023. "Robust investment and hedging policy with limited commitment," Economic Modelling, Elsevier, vol. 125(C).
    19. Wu, Wei & Niu, Yingjie & Wu, Yaoyao & Xu, Hongru, 2022. "Ambiguity, limited commitment, and the q theory of investment," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    20. Dirk Krueger & Harald Uhlig, 2024. "Neoclassical Growth with Limited Commitment," PIER Working Paper Archive 22-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    21. 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.
    22. Ai, Hengjie & Li, Rui, 2015. "Investment and CEO compensation under limited commitment," Journal of Financial Economics, Elsevier, vol. 116(3), pages 452-472.

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    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

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