IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v177y2024ics0304414924001546.html
   My bibliography  Save this article

Principal-Multiagents problem under equivalent changes of measure: General study and an existence result

Author

Listed:
  • Hernández-Santibáñez, Nicolás

Abstract

We study a general contracting problem between the principal and a finite set of competitive agents, who perform equivalent changes of measure by controlling the drift of the output process and the compensator of its associated jump measure. In this setting, we generalize the dynamic programming approach developed by Cvitanić et al. (2018) and we also relax their assumptions. We prove that the problem of the principal can be reformulated as a standard stochastic control problem in which she controls the continuation utility (or certainty equivalent) processes of the agents. Our assumptions and conditions on the admissible contracts are minimal to make our approach work. We review part of the literature and give examples on how they are usually satisfied. We also present a smoothness result for the value function of a risk–neutral principal when the agents have exponential utility functions. This leads, under some additional assumptions, to the existence of an optimal contract.

Suggested Citation

  • Hernández-Santibáñez, Nicolás, 2024. "Principal-Multiagents problem under equivalent changes of measure: General study and an existence result," Stochastic Processes and their Applications, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:spapps:v:177:y:2024:i:c:s0304414924001546
    DOI: 10.1016/j.spa.2024.104448
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924001546
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104448?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    2. Henri Pages & Dylan Possamaï, 2014. "A mathematical treatment of bank monitoring incentives," Finance and Stochastics, Springer, vol. 18(1), pages 39-73, January.
    3. Fujii, Masaaki & Takahashi, Akihiko, 2018. "Quadratic–exponential growth BSDEs with jumps and their Malliavin’s differentiability," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2083-2130.
    4. repec:dau:papers:123456789/5371 is not listed on IDEAS
    5. Hu, Ying & Tang, Shanjian, 2016. "Multi-dimensional backward stochastic differential equations of diagonally quadratic generators," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1066-1086.
    6. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-364, June.
    7. Bastien Baldacci & Dylan Possamai & Mathieu Rosenbaum, 2019. "Optimal make take fees in a multi market maker environment," Papers 1907.11053, arXiv.org, revised Mar 2021.
    8. Steven Shavell, 1979. "Risk Sharing and Incentives in the Principal and Agent Relationship," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 55-73, Spring.
    9. Dilip Mookherjee, 1984. "Optimal Incentive Schemes with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 433-446.
    10. 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.
    11. Briand, Philippe & Elie, Romuald, 2013. "A simple constructive approach to quadratic BSDEs with or without delay," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2921-2939.
    12. 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.
    13. 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.
    14. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    15. Demski, Joel S. & Sappington, David, 1984. "Optimal incentive contracts with multiple agents," Journal of Economic Theory, Elsevier, vol. 33(1), pages 152-171, June.
    16. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    17. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.
    18. Carlier, G. & Dana, R.-A., 2005. "Existence and monotonicity of solutions to moral hazard problems," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 826-843, November.
    19. Sarah Bensalem & Nicolás Hernández-Santibáñez & Nabil Kazi-Tani, 2023. "A continuous-time model of self-protection," Finance and Stochastics, Springer, vol. 27(2), pages 503-537, April.
    20. Moroni, Sofia & Swinkels, Jeroen, 2014. "Existence and non-existence in the moral hazard problem," Journal of Economic Theory, Elsevier, vol. 150(C), pages 668-682.
    21. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
    22. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
    Full references (including those not matched with items on IDEAS)

    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. Daniel Krv{s}ek & Dylan Possamai, 2023. "Randomisation with moral hazard: a path to existence of optimal contracts," Papers 2311.13278, arXiv.org.
    2. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2020. "Bank Monitoring Incentives Under Moral Hazard and Adverse Selection," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 988-1035, March.
    3. Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    4. Thibaut Mastrolia & Dylan Possamaï, 2018. "Moral Hazard Under Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 452-500, November.
    5. Romuald Élie & Emma Hubert & Thibaut Mastrolia & Dylan Possamaï, 2021. "Mean–field moral hazard for optimal energy demand response management," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 399-473, January.
    6. Inés Macho-Stadler & David Pérez-Castrillo, 2018. "Moral hazard: Base models and two extensions," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 16, pages 453-485, Edward Elgar Publishing.
    7. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Post-Print hal-04164688, HAL.
    8. Fleckinger, Pierre, 2012. "Correlation and relative performance evaluation," Journal of Economic Theory, Elsevier, vol. 147(1), pages 93-117.
    9. Nicol'as Hern'andez Santib'a~nez & Dylan Possamai & Chao Zhou, 2017. "Bank monitoring incentives under moral hazard and adverse selection," Papers 1701.05864, arXiv.org, revised Jan 2019.
    10. Dylan Possamai & Chiara Rossato, 2023. "Golden parachutes under the threat of accidents," Papers 2312.02101, arXiv.org, revised Dec 2024.
    11. Rongzhu Ke & Xinyi Xu, 2023. "The existence of an optimal deterministic contract in moral hazard problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 375-416, August.
    12. Romuald Elie & Emma Hubert & Thibaut Mastrolia & Dylan Possamai, 2019. "Mean-field moral hazard for optimal energy demand response management," Papers 1902.10405, arXiv.org, revised Mar 2020.
    13. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.
    14. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    15. 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.
    16. Alex Edmans & Xavier Gabaix, 2016. "Executive Compensation: A Modern Primer," Journal of Economic Literature, American Economic Association, vol. 54(4), pages 1232-1287, December.
    17. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    18. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2020. "Bank monitoring incentives under moral hazard and adverse selection," Post-Print hal-01435460, HAL.
    19. Alessandro Chiusolo & Emma Hubert, 2024. "A new approach to principal-agent problems with volatility control," Papers 2407.09471, arXiv.org.
    20. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.

    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:eee:spapps:v:177:y:2024:i:c:s0304414924001546. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.