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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. M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 382-387.
  2. Pagès, H., 2009. "Bank incentives and optimal CDOs," Working papers 253, Banque de France.
  3. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 30-54.
  4. 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.
  5. 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.
  6. Skrzypacz, Andrzej & Sannikov, Yuliy, 2005. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," Research Papers 1887, Stanford University, Graduate School of Business.
  7. Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
  8. 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.
  9. 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.
  10. Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean Charles, 2004. "Dynamic Security Design," CEPR Discussion Papers 4753, C.E.P.R. Discussion Papers.
  11. 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.
  12. 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.
  13. 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.
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  15. 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.
  16. 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.
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Cited by:
  1. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 30-54.

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