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.
References listed on IDEAS
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.:
- 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.
- 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..
- Yuliy Sannikov & Andrzej Skrzypacz, 2004.
"Impossibility of Collusion under Imperfect Monitoring with Flexible Production,"
2004 Meeting Papers
418, Society for Economic Dynamics.
- Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December.
- Skrzypacz, Andrzej & Sannikov, Yuliy, 2005. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," Research Papers 1887, Stanford University, Graduate School of Business.
- 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.
- Pagès, H., 2012.
"Bank monitoring incentives and optimal ABS,"
377, Banque de France.
- Yuliy Sannikov & Andrzej Skrzypacz, 2006.
"The role of information in repeated games with frequent actions,"
2006 Meeting Papers
871, Society for Economic Dynamics.
- Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, vol. 78(3), pages 847-882, 05.
- 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.
- 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.
- David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988.
"Information and Timing in Repeated Partnerships,"
Cowles Foundation Discussion Papers
875, Cowles Foundation for Research in Economics, Yale University.
- Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & Stéphane Villeneuve, 2010.
"Large risks, limited liability, and dynamic moral hazard,"
- Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010. "Large Risks, Limited Liability, and Dynamic Moral Hazard," Econometrica, 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.
- 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.
- 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.
- Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean-Charles, 2004.
"Dynamic Security Design,"
CEPR Discussion Papers
4753, C.E.P.R. Discussion Papers.
- Rüdiger Frey & Jochen Backhaus, 2008. "Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
- Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015.
"Modeling financial contagion using mutually exciting jump processes,"
Journal of Financial Economics,
Elsevier, vol. 117(3), pages 585-606.
- Yacine Aït-Sahalia & Julio Cacho-Diaz & Roger J.A. Laeven, 2010. "Modeling Financial Contagion Using Mutually Exciting Jump Processes," NBER Working Papers 15850, National Bureau of Economic Research, Inc.
- M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 382-387.
- Fan Yu, 2007. "Correlated Defaults In Intensity-Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173.
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 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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.