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A mathematical treatment of bank monitoring incentives

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  • Possamaï, Dylan
  • Pagès, Henri

Abstract

In this paper, we take up the analysis of a principal/agent model with moral hazard introduced by Pagès (J. Financ. Intermed. doi:10.1016/j.jfi.2012.06.001, 2012), 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, Springer 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.

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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/12313.

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Handle: RePEc:dau:papers:123456789/12313

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Keywords: Verification theorem; Stochastic control; Optimal securitization; Optimal incentives; Dynamic moral hazard; Principal/agent problem;

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References

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  1. Yuliy Sannikov & Andrzej Skrzypacz, 2004. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," 2004 Meeting Papers, Society for Economic Dynamics 418, Society for Economic Dynamics.
  2. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1713-33, November.
  3. Adam B. Ashcraft & Til Schuermann, 2008. "Understanding the securitization of subprime mortgage credit," Staff Reports, Federal Reserve Bank of New York 318, Federal Reserve Bank of New York.
  4. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, Elsevier, vol. 22(1), pages 30-54.
  5. 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.
  6. 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.
  7. 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.
  8. Yuliy Sannikov & Andrzej Skrzypacz, 2006. "The role of information in repeated games with frequent actions," 2006 Meeting Papers, Society for Economic Dynamics 871, Society for Economic Dynamics.
  9. Pagès, H., 2009. "Bank incentives and optimal CDOs," Working papers, Banque de France 253, Banque de France.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(4), pages 382-387.
  16. 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.
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Cited by:
  1. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, Elsevier, vol. 22(1), pages 30-54.

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