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The Risk-Sharing Problem Under Limited Liability Constraints in a Single-Period Model

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  • Jessica Martin

    (INSA de Toulouse, IMT UMR CNRS 5219, Université de Toulouse)

Abstract

This work provides analysis of a variant of the Risk-Sharing Principal-Agent problem in a single period setting with additional constant lower and upper bounds on the wage paid to the Agent. The effect of the extra constraints on optimal contract existence is studied and leads to conditions on the underlying utility functions under which an optimum may be attained. Solution characterization is then provided along with the derivation of a Borch rule for Limited Liability. Finally, some applications, including the CARA utility case, are discussed.

Suggested Citation

  • Jessica Martin, 2021. "The Risk-Sharing Problem Under Limited Liability Constraints in a Single-Period Model," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 854-872, June.
  • Handle: RePEc:spr:joptap:v:189:y:2021:i:3:d:10.1007_s10957-021-01861-8
    DOI: 10.1007/s10957-021-01861-8
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    References listed on IDEAS

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    1. Page, Frank Jr., 1987. "The existence of optimal contracts in the principal-agent model," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 157-167, April.
    2. James A. Mirrlees, 1976. "The Optimal Structure of Incentives and Authority Within an Organization," Bell Journal of Economics, The RAND Corporation, vol. 7(1), pages 105-131, Spring.
    3. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    4. Ohad Kadan & Philip J. Reny & Jeroen M. Swinkels, 2017. "Existence of Optimal Mechanisms in Principal‐Agent Problems," Econometrica, Econometric Society, vol. 85, pages 769-823, May.
    5. Kadan, Ohad & Swinkels, Jeroen M., 2013. "Minimum payments and induced effort in moral hazard problems," Games and Economic Behavior, Elsevier, vol. 82(C), pages 468-489.
    6. Mathias Dewatripont & Patrick Legros & Steven A. Matthews, 2003. "Moral Hazard and Capital Structure Dynamics," Journal of the European Economic Association, MIT Press, vol. 1(4), pages 890-930, June.
    7. Matthews, Steven A., 2001. "Renegotiating Moral Hazard Contracts under Limited Liability and Monotonicity," Journal of Economic Theory, Elsevier, vol. 97(1), pages 1-29, March.
    8. Eun‐Soo Park, 1995. "Incentive Contracting Under Limited Liability," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 477-490, September.
    9. Sappington, David, 1983. "Limited liability contracts between principal and agent," Journal of Economic Theory, Elsevier, vol. 29(1), pages 1-21, February.
    10. Ross, Stephen A, 1973. "The Economic Theory of Agency: The Principal's Problem," American Economic Review, American Economic Association, vol. 63(2), pages 134-139, May.
    11. Jewitt, Ian & Kadan, Ohad & Swinkels, Jeroen M., 2008. "Moral hazard with bounded payments," Journal of Economic Theory, Elsevier, vol. 143(1), pages 59-82, November.
    12. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    13. Park, Eun-Soo, 1995. "Incentive Contracting under Limited Liability," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 477-490, Fall.
    14. Son Ku Kim, 1997. "Limited Liability and Bonus Contracts," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(4), pages 899-913, December.
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