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A mathematical treatment of bank monitoring incentives

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  • Henri Pag\`es
  • Dylan Possamai

Abstract

In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in \cite{pages}, 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 \cite{san} how the maximization problem with implicit constraints faced by investors can be reduced to a classic stochastic control problem. The approach has the advantage of avoiding the more general techniques based on forward-backward stochastic differential equations described in \cite{cviz} 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.

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Paper provided by arXiv.org in its series Papers with number 1202.2076.

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Date of creation: Feb 2012
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Handle: RePEc:arx:papers:1202.2076

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  1. 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.
  2. Pagès, H., 2012. "Bank monitoring incentives and optimal ABS," Working papers, Banque de France 377, Banque de France.
  3. Skrzypacz, Andrzej & Sannikov, Yuliy, 2005. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," Research Papers, Stanford University, Graduate School of Business 1887, Stanford University, Graduate School of Business.
  4. Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, Econometric Society, vol. 78(3), pages 847-882, 05.
  5. Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean Charles, 2004. "Dynamic Security Design," CEPR Discussion Papers, C.E.P.R. Discussion Papers 4753, C.E.P.R. Discussion Papers.
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  8. 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.
  9. Biais, Bruno & Mariotti, Thomas & Rochet, Jean-Charles & Villeneuve, Stéphane, 2007. "Large Risks, Limited Liability and Dynamic Moral Hazard," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 472, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2009.
  10. 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.
  11. Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
  12. 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., World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
  13. 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, American Finance Association, vol. 61(6), pages 2681-2724, December.
  14. Peter M. DeMarzo & Michael J. Fishman, 2007. "Agency and Optimal Investment Dynamics," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 20(1), pages 151-188, January.
  15. Robert A. Jarrow, 2001. "Counterparty Risk and the Pricing of Defaultable Securities," Journal of Finance, American Finance Association, American Finance Association, vol. 56(5), pages 1765-1799, October.
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Cited by:
  1. Pagès, H., 2012. "Bank monitoring incentives and optimal ABS," Working papers, Banque de France 377, Banque de France.

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