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Risk-sharing and optimal contracts with large exogenous risks

Author

Listed:
  • Jessica Martin

    (Université de Toulouse)

  • Stéphane Villeneuve

    (Université Toulouse 1 Capitole, (TSE-TSMR))

Abstract

We consider a dynamic principal–agent model that naturally extends the classical Holmström–Milgrom setting to include a risk capable of stopping production completely. We obtain an explicit characterization of the optimal wage along with the optimal action provided by the agent. The optimal contract is linear by offering both a fixed share of the output which is similar to the standard Holmström–Milgrom model and a linear prevention mechanism that is proportional to the random lifetime of the contract. We then extend the model by allowing insurable risks where the agent can control the intensity of the failure by exerting an additional costly effort.

Suggested Citation

  • Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 1-43, June.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:1:d:10.1007_s10203-023-00386-1
    DOI: 10.1007/s10203-023-00386-1
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    References listed on IDEAS

    as
    1. Henri Pages & Dylan Possamaï, 2014. "A mathematical treatment of bank monitoring incentives," Finance and Stochastics, Springer, vol. 18(1), pages 39-73, January.
    2. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November.
    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. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    5. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    6. Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010. "Large Risks, Limited Liability, and Dynamic Moral Hazard," Econometrica, Econometric Society, vol. 78(1), pages 73-118, January.
    7. repec:dau:papers:123456789/9697 is not listed on IDEAS
    8. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    9. Yiqing Lin & Zhenjie Ren & Nizar Touzi & Junjian Yang, 2020. "Random horizon principal-agent problems," Papers 2002.10982, arXiv.org, revised Feb 2022.
    10. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
    11. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    12. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
    13. Schattler, Heinz & Sung, Jaeyoung, 1997. "On optimal sharing rules in discrete-and continuous-time principal-agent problems with exponential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 551-574.
    14. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 599-617.
    15. Sung, Jaeyoung, 1997. "Corporate Insurance and Managerial Incentives," Journal of Economic Theory, Elsevier, vol. 74(2), pages 297-332, June.
    16. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
    17. Jakša Cvitanić & Xuhu Wan & Jianfeng Zhang, 2006. "Optimal contracts in continuous-time models," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-27, July.
    18. Pham, Huyên, 2010. "Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1795-1820, August.
    19. repec:dau:papers:123456789/12313 is not listed on IDEAS
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    More about this item

    Keywords

    Principal–agent problems; Risk-sharing; Hamilton–Jacobi–Bellman equations;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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