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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, September.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:1:d:10.1007_s11579-024-00378-8
    DOI: 10.1007/s11579-024-00378-8
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    References listed on IDEAS

    as
    1. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2017. "Moral Hazard in Dynamic Risk Management," Management Science, INFORMS, vol. 63(10), pages 3328-3346, October.
    2. 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.
    3. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    4. 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.
    5. Yiqing Lin & Zhenjie Ren & Nizar Touzi & Junjian Yang, 2020. "Random horizon principal-agent problems," Papers 2002.10982, arXiv.org, revised Feb 2022.
    6. Cvitanić, Jakša & Xing, Hao, 2018. "Asset pricing under optimal contracts," Journal of Economic Theory, Elsevier, vol. 173(C), pages 142-180.
    7. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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    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

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