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A Continuous-Time Agency Model of Optimal Contracting and Capital Structure


  • Peter M. DeMarzo
  • Yuliy Sannikov


We consider a principal-agent model in which the agent needs to raise capital from the principal to finance a project. Our model is based on DeMarzo and Fishman (2003), except that the agent's cash flows are given by a Brownian motion with drift in continuous time. The difficulty in writing an appropriate financial contract in this setting is that the agent can conceal and divert cash flows for his own consumption rather than pay back the principal. Alternatively, the agent may reduce the mean of cash flows by not putting in effort. To give the agent incentives to provide effort and repay the principal, a long-term contract specifies the agent's wage and can force termination of the project. Using techniques from stochastic calculus similar to Sannikov (2003), we characterize the optimal contract by a differential equation. We show that this contract is equivalent to the limiting case of a discrete time model with binomial cash flows. The optimal contract can be interpreted as a combination of equity, a credit line, and either long-term debt or a compensating balance requirement (i.e., a cash position). The project is terminated if the agent exhausts the credit line and defaults. Once the credit line is paid off, excess cash flows are used to pay dividends. The agent is compensated with equity alone. Unlike the discrete time setting, our differential equation for the continuous-time model allows us to compute contracts easily, as well as compute comparative statics. The model provides a simple dynamic theory of security design and optimal capital structure.

Suggested Citation

  • 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.
  • Handle: RePEc:nbr:nberwo:10615
    Note: CF AP

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    References listed on IDEAS

    1. Rui Albuquerque & Hugo A. Hopenhayn, 2004. "Optimal Lending Contracts and Firm Dynamics," Review of Economic Studies, Oxford University Press, vol. 71(2), pages 285-315.
    2. Phelan, C. & Townsend, R.M., 1990. "Computing Multiperiod, Information-Constrained Optima," University of Chicago - Economics Research Center 90-13, Chicago - Economics Research Center.
    3. Christopher Phelan & Robert M. Townsend, 1991. "Computing Multi-Period, Information-Constrained Optima," Review of Economic Studies, Oxford University Press, vol. 58(5), pages 853-881.
    4. Peter M. DeMarzo & Michael J. Fishman, 2007. "Agency and Optimal Investment Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 151-188, January.
    5. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-1089, July.
    6. Peter M. DeMarzo & Michael J. Fishman, 2007. "Optimal Long-Term Financial Contracting," Review of Financial Studies, Society for Financial Studies, vol. 20(6), pages 2079-2128, November.
    7. 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.
    8. Hui Ou-Yang, 2003. "Optimal Contracts in a Continuous-Time Delegated Portfolio Management Problem," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 173-208.
    9. Oliver Hart & John Moore, 1994. "A Theory of Debt Based on the Inalienability of Human Capital," The Quarterly Journal of Economics, Oxford University Press, vol. 109(4), pages 841-879.
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    Cited by:

    1. Hui Chen & Jianjun Miao & Neng Wang, 2010. "Entrepreneurial Finance and Nondiversifiable Risk," Review of Financial Studies, Society for Financial Studies, vol. 23(12), pages 4348-4388, December.

    More about this item

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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