A mathematical treatment of bank monitoring incentives
In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in , with optimal contracting between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian contagion. We provide here a comprehensive mathematical formulation of the model and show using martingale arguments in the spirit of Sannikov  how the maximization problem with implicit constraints faced by investors can be reduced to a classical stochastic control problem. The approach has the advantage of avoiding the more general techniques based on forward-backward stochastic differential equations described in  and leads to a simple recursive system of Hamilton-Jacobi-Bellman equations. We provide a solution to our problem by a verification argument and give an explicit description of both the value function and the optimal contract. Finally, we study the limit case where the bank is no longer impatient.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010.
"Large Risks, Limited Liability, and Dynamic Moral Hazard,"
Econometric Society, vol. 78(1), pages 73-118, 01.
- Biais, Bruno & Mariotti, Thomas & Rochet, Jean-Charles & Villeneuve, Stéphane, 2007. "Large Risks, Limited Liability and Dynamic Moral Hazard," IDEI Working Papers 472, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2009.
- Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & Stéphane Villeneuve, 2010. "Large risks, limited liability, and dynamic moral hazard," Post-Print halshs-00491470, HAL.
- Ashcraft, Adam B. & Schuermann, Til, 2008.
"Understanding the Securitization of Subprime Mortgage Credit,"
Foundations and Trends(R) in Finance,
now publishers, vol. 2(3), pages 191-309, June.
- Adam B. Ashcraft & Til Schuermann, 2008. "Understanding the securitization of subprime mortgage credit," Staff Reports 318, Federal Reserve Bank of New York.
- Robert A. Jarrow & Fan Yu, 2008.
"Counterparty Risk and the Pricing of Defaultable Securities,"
World Scientific Book Chapters,
in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515
World Scientific Publishing Co. Pte. Ltd..
- Robert A. Jarrow, 2001. "Counterparty Risk and the Pricing of Defaultable Securities," Journal of Finance, American Finance Association, vol. 56(5), pages 1765-1799, October.
- Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007.
"Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications,"
Review of Economic Studies,
Oxford University Press, vol. 74(2), pages 345-390.
- Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean-Charles, 2004. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," IDEI Working Papers 312, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2006.
- 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.
- Fan Yu, 2007. "Correlated Defaults In Intensity-Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173.
- PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous-Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
- M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 382-387.
- Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 957-984.
- Guillaume Plantin & Bruno Biais & Thomas Mariotti & Jean-Charles Rochet, 2004.
"Dynamic Security Design,"
GSIA Working Papers
2005-E5, Carnegie Mellon University, Tepper School of Business.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1202.2076. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.