IDEAS home Printed from https://ideas.repec.org/b/spr/mathfi/v19y2025i1d10.1007_s11579-024-00378-8.html
   My bibliography  Save this book

A note on persistent private information

Author

Listed:
  • Beatrice Acciaio

    (ETH Zürich)

  • Robert A. Crowell

    (ETH Zürich)

  • Jakša Cvitanić

    (Division of the Humanities and Social Sciences)

Abstract

We study the contracting problem in the persistent private information model of Williams [17], in which an agent provides a report of a privately observed path to the principal, who in turn pays the agent in the least expensive way that induces truthful reporting. We first argue that, in the case of persistent information, the contract in [17] does not induce truthful reporting if misreporting is allowed to grow sufficiently fast. The contract becomes incentive compatible (i.e., induces truthful reporting) if one imposes additional restrictions on misreporting, as shown also in Bloedel, Krishna, and Strulovici [2] under conditions different from ours. Under such restrictions, we show that the contract identified in [2] is optimal among linear contracts. On the other hand, if additional restrictions are not imposed, we show that the contract optimal in a family of generalized linear contracts is deterministic.

Suggested Citation

  • Beatrice Acciaio & Robert A. Crowell & Jakša Cvitanić, 2025. "A note on persistent private information," Mathematics and Financial Economics, Springer, volume 19, number 5, December.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:1:d:10.1007_s11579-024-00378-8
    DOI: 10.1007/s11579-024-00378-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11579-024-00378-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11579-024-00378-8?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. 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.
    2. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    3. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    4. Guillermo Alonso Alvarez & Sergey Nadtochiy, 2023. "Optimal contract design via relaxation: application to the problem of brokerage fee for a client with private signal," Papers 2307.07010, arXiv.org.
    5. Yiqing Lin & Zhenjie Ren & Nizar Touzi & Junjian Yang, 2020. "Random horizon principal-agent problems," Papers 2002.10982, arXiv.org, revised Feb 2022.
    6. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2017. "Moral Hazard in Dynamic Risk Management," Management Science, INFORMS, vol. 63(10), pages 3328-3346, October.
    7. Cvitanić, Jakša & Xing, Hao, 2018. "Asset pricing under optimal contracts," Journal of Economic Theory, Elsevier, vol. 173(C), pages 142-180.
    8. 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.
    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. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.
    3. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    4. Emma Hubert & Thibaut Mastrolia & Dylan Possamai & Xavier Warin, 2020. "Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemic," Papers 2009.00484, arXiv.org, revised Apr 2022.
    5. Dou, Zheng & Lai, Chong, 2025. "Risk-incentive trade-off in moral hazard with risk management: Theoretical analysis and empirical verification," Economic Modelling, Elsevier, vol. 148(C).
    6. Camilo Hernández & Dylan Possamaï, 2024. "Time‐inconsistent contract theory," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 1022-1085, July.
    7. Jean-Paul Décamps & Stéphane Villeneuve, 2019. "A two-dimensional control problem arising from dynamic contracting theory," Finance and Stochastics, Springer, vol. 23(1), pages 1-28, January.
    8. 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.
    9. Camilo Hern'andez & Dylan Possamai, 2023. "Time-inconsistent contract theory," Papers 2303.01601, arXiv.org.
    10. Martin Dumav, 2021. "Moral Hazard, Dynamic Incentives, and Ambiguous Perceptions," Papers 2110.15229, arXiv.org.
    11. Alessandro Chiusolo & Emma Hubert, 2024. "A new approach to principal-agent problems with volatility control," Papers 2407.09471, arXiv.org, revised Jun 2025.
    12. Tak-Yuen Wong, 2019. "Dynamic Agency and Endogenous Risk-Taking," Management Science, INFORMS, vol. 65(9), pages 4032-4048, September.
    13. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.
    14. Thibaut Mastrolia & Dylan Possamaï, 2018. "Moral Hazard Under Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 452-500, November.
    15. 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.
    16. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Post-Print hal-04164688, HAL.
    17. Thibaut Mastrolia & Tianrui Xu, 2025. "Optimal Rebate Design: Incentives, Competition and Efficiency in Auction Markets," Papers 2501.12591, arXiv.org.
    18. Piskorski, Tomasz & Westerfield, Mark M., 2016. "Optimal dynamic contracts with moral hazard and costly monitoring," Journal of Economic Theory, Elsevier, vol. 166(C), pages 242-281.
    19. Dylan Possamai & Chiara Rossato, 2023. "Golden parachutes under the threat of accidents," Papers 2312.02101, arXiv.org, revised Dec 2024.
    20. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.

    More about this item

    Keywords

    Principal-Agent problem; Persistent information; Truthful reporting; Incentive-compatible contracts;
    All these keywords.

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G00 - Financial Economics - - General - - - General
    • G30 - Financial Economics - - Corporate Finance and Governance - - - General
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

    Statistics

    Access and download statistics

    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:spr:mathfi:v:19:y:2025:i:1:d:10.1007_s11579-024-00378-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.