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A mathematical treatment of bank monitoring incentives

  • Henri Pages

    ()

  • Dylan Possamaï

    ()

In this paper, we take up the analysis of a principal/agent model with moral hazard introduced by Pages (J. Financ. Intermed.), 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 (Rev. Econ. Stud. 75:957–984, 2008), 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 by Cvitanić and Zhang (Contract Theory in Continuous Time Models, 2012) 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. Copyright Springer-Verlag Berlin Heidelberg 2014

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File URL: http://hdl.handle.net/10.1007/s00780-013-0202-y
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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 18 (2014)
Issue (Month): 1 (January)
Pages: 39-73

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Handle: RePEc:spr:finsto:v:18:y:2014:i:1:p:39-73
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  1. 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.
  2. Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & Stéphane Villeneuve, 2010. "Large risks, limited liability, and dynamic moral hazard," Working Papers 245707, Institut National de la Recherche Agronomique, France.
  3. 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.
  4. 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.
  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. Pagès, H., 2012. "Bank monitoring incentives and optimal ABS," Working papers 377, Banque de France.
  7. 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.
  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. 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.
  10. Adam B. Ashcraft & Til Schuermann, 2008. "Understanding the securitization of subprime mortgage credit," Staff Reports 318, Federal Reserve Bank of New York.
  11. Yuliy Sannikov & Andrzej Skrzypacz, 2006. "The role of information in repeated games with frequent actions," 2006 Meeting Papers 871, Society for Economic Dynamics.
  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.
  14. Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
  15. M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 382-387.
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