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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 [17], 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 [18] 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 [6] 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.

Suggested Citation

  • Henri Pag`es & Dylan Possamai, 2012. "A mathematical treatment of bank monitoring incentives," Papers 1202.2076, arXiv.org, revised Apr 2015.
  • Handle: RePEc:arx:papers:1202.2076
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    References listed on IDEAS

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    1. 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, January.
    2. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    3. 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.
    4. 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.
    5. Biais, Bruno & Mariotti, Thomas & Plantin, Guillaume & Rochet, Jean-Charles, 2004. "Dynamic Security Design," CEPR Discussion Papers 4753, C.E.P.R. Discussion Papers.
    6. Pagès, H., 2009. "Bank incentives and optimal CDOs," Working papers 253, Banque de France.
    7. Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, vol. 78(3), pages 847-882, May.
    8. 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.
    9. Fan Yu, 2007. "Correlated Defaults In Intensity-Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173.
    10. M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 382-387.
    11. 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.
    12. 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..
    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. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 30-54.
    15. 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.
    16. 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.
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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.
    2. Nicol'as Hern'andez Santib'a~nez & Dylan Possamai & Chao Zhou, 2017. "Bank monitoring incentives under moral hazard and adverse selection," Papers 1701.05864, arXiv.org, revised Feb 2018.
    3. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2017. "Bank monitoring incentives under moral hazard and adverse selection," Working Papers hal-01435460, HAL.

    More about this item

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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