IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v8y2008i1n23.html
   My bibliography  Save this article

Principal-Agent Problems with Exit Options

Author

Listed:
  • Cvitanic Jaksa

    (Caltech, cvitanic@hss.caltech.edu)

  • Wan Xuhu

    (Hong Kong University of Science and Technology, imwan@ust.hk)

  • Zhang Jianfeng

    (University of Southern California, jianfenz@usc.edu)

Abstract

We consider the problem of when to deliver the contract payoff, in a continuous-time principal-agent setting, in which the agent's effort is unobservable. The principal can design contracts of a simple form that induce the agent to ask for the payoff at the time of the principal's choosing. The optimal time of payment depends on the agent's and the principal's outside options. We develop a theory for general utility functions, while with CARA utilities we are able to specify conditions under which the optimal payment time is not random. However, in general, the optimal payment time is typically random. One illustrative application is the case when the agent can be fired, after having been paid a severance payment, and then replaced by another agent. The methodology we use is the stochastic maximum principle and its link to Forward-Backward Stochastic Differential Equations.

Suggested Citation

  • Cvitanic Jaksa & Wan Xuhu & Zhang Jianfeng, 2008. "Principal-Agent Problems with Exit Options," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-43, October.
    • Handle: RePEc:bpj:bejtec:v:8:y:2008:i:1:n:23
    DOI: 10.2202/1935-1704.1474
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1935-1704.1474
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1935-1704.1474?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. Wang, Cheng, 2011. "Termination of dynamic contracts in an equilibrium labor market model," Journal of Economic Theory, Elsevier, vol. 146(1), pages 74-110, January.
    2. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, April.
    3. Muller, Holger M., 1998. "The First-Best Sharing Rule in the Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, Elsevier, vol. 79(2), pages 276-280, April.
    4. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    5. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    6. Jaeyoung Sung, 2005. "Optimal Contracts Under Adverse Selection and Moral Hazard: A Continuous-Time Approach," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 1021-1073.
    7. Muller, Holger M., 2000. "Asymptotic Efficiency in Dynamic Principal-Agent Problems," Journal of Economic Theory, Elsevier, vol. 91(2), pages 292-301, April.
    8. 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.
    9. 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.
    10. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    11. Thomas Philippon & Yuliy Sannikov, 2007. "Real Options in a Dynamic Agency Model, with Applications to Financial Development, IPOs, and Business Risk," NBER Working Papers 13584, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohamed Belhaj & Nataliya Klimenko, 2012. "Optimal Preventive Bank Supervision Combining Random Audits and Continuous Intervention," AMSE Working Papers 1201, Aix-Marseille School of Economics, France.
    2. Barlo, Mehmet & Özdog˜an, Ayça, 2014. "Optimality of linearity with collusion and renegotiation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 46-52.
    3. Sheng, Jichuan & Webber, Michael, 2018. "Using incentives to coordinate responses to a system of payments for watershed services: The middle route of South–North Water Transfer Project, China," Ecosystem Services, Elsevier, vol. 32(PA), pages 1-8.
    4. Sheng, Jichuan, 2019. "Neoliberal environmentality and incentive-coordinated REDD+ contracts," Land Use Policy, Elsevier, vol. 81(C), pages 400-407.
    5. Cvitanic, Jaksa & Radas, Sonja & Sikic, Hrvoje, 2011. "Co-development ventures: Optimal time of entry and profit-sharing," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1710-1730, October.
    6. Sheng, Jichuan & Hong, Qiu & Han, Xiao, 2019. "Neoliberal conservation in REDD+: The roles of market power and incentive designs," Land Use Policy, Elsevier, vol. 89(C).
    7. Patrick Bolton & Christopher Harris, 2005. "The Dynamics of Optimal Risk Sharing," Economics Working Papers 0092, Institute for Advanced Study, School of Social Science, revised May 2010.
    8. Guillermo Alonso Alvarez & Erhan Bayraktar & Ibrahim Ekren & Liwei Huang, 2024. "Sequential optimal contracting in continuous time," Papers 2411.04262, arXiv.org.
    9. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    10. Benedetti, Giuseppe, 2013. "Investissement optimal et évaluation d'actifs sous certaines imperfections de marché," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/12887 edited by Campi, Luciano.
    11. Sheng, Jichuan & Yang, Hongqiang, 2024. "Linking water markets with payments for watershed services: the eastern route of China's South-North Water Transfer Project," Agricultural Water Management, Elsevier, vol. 295(C).
    12. Cuoco, Domenico & Kaniel, Ron, 2011. "Equilibrium prices in the presence of delegated portfolio management," Journal of Financial Economics, Elsevier, vol. 101(2), pages 264-296, August.
    13. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    14. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.
    15. Peter M. DeMarzo & Yuliy Sannikov, 2004. "A Continuous-Time Agency Model of Optimal Contracting and Capital Structure," NBER Working Papers 10615, National Bureau of Economic Research, Inc.
    16. Sheng, Jichuan & Qiu, Hong, 2018. "Governmentality within REDD+: Optimizing incentives and efforts to reduce emissions from deforestation and degradation," Land Use Policy, Elsevier, vol. 76(C), pages 611-622.

    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. Egil Matsen, 2005. "Portfolio choice when managers control returns," Working Paper 2005/15, Norges Bank.
    2. Jakv{s}a Cvitani'c & Dylan Possamai & Nizar Touzi, 2015. "Dynamic programming approach to principal-agent problems," Papers 1510.07111, arXiv.org, revised Jan 2017.
    3. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    4. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    5. 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.
    6. Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    7. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    8. 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.
    9. Jakša Cvitanić & Xuhu Wan & Huali Yang, 2013. "Dynamics of Contract Design with Screening," Management Science, INFORMS, vol. 59(5), pages 1229-1244, May.
    10. Jaeyoung Sung, 2022. "Optimal contracting under mean-volatility joint ambiguity uncertainties," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 593-642, September.
    11. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Post-Print hal-04164688, HAL.
    12. Barlo, Mehmet & Özdog˜an, Ayça, 2014. "Optimality of linearity with collusion and renegotiation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 46-52.
    13. Muller, Holger M., 1998. "The First-Best Sharing Rule in the Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, Elsevier, vol. 79(2), pages 276-280, April.
    14. 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.
    15. Araujo, Aloisio & Moreira, Humberto & Tsuchida, Marcos, 2007. "The Trade-Off Between Incentives and Endogenous Risk," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 27(2), November.
    16. Kerem Ugurlu, 2018. "Dynamic optimal contract under parameter uncertainty with risk averse agent and principal," Papers 1806.01495, arXiv.org.
    17. Camilo Hern'andez & Dylan Possamai, 2023. "Time-inconsistent contract theory," Papers 2303.01601, arXiv.org.
    18. Jaeyoung Sung, 2005. "Optimal Contracts Under Adverse Selection and Moral Hazard: A Continuous-Time Approach," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 1021-1073.
    19. Giat, Yahel & Subramanian, Ajay, 2013. "Dynamic contracting under imperfect public information and asymmetric beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2833-2861.
    20. Muller, Holger M., 2000. "Asymptotic Efficiency in Dynamic Principal-Agent Problems," Journal of Economic Theory, Elsevier, vol. 91(2), pages 292-301, April.

    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:bpj:bejtec:v:8:y:2008:i:1:n:23. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.