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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. 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.
    2. Pagès, H., 2009. "Bank incentives and optimal CDOs," Working papers 253, Banque de France.
    3. Fan Yu, 2007. "Correlated Defaults In Intensity‐Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173, April.
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    7. 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.
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    12. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 30-54.
    13. J.-P. Laurent & A. Cousin & J.-D. Fermanian, 2011. "Hedging default risks of CDOs in Markovian contagion models," Quantitative Finance, Taylor & Francis Journals, vol. 11(12), pages 1773-1791.
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    15. 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.
    16. 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..
    17. Jean-Paul Laurent & Areski Cousin & Jean-David Fermanian, 2011. "Hedging default risks of CDOs in Markovian contagion models," Post-Print hal-03676198, HAL.
    18. 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.
    19. 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.
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    Cited by:

    1. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Post-Print hal-04164688, HAL.
    2. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 30-54.
    3. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2020. "Bank monitoring incentives under moral hazard and adverse selection," Post-Print hal-01435460, HAL.
    4. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2020. "Bank Monitoring Incentives Under Moral Hazard and Adverse Selection," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 988-1035, March.
    5. Thibaut Mastrolia & Dylan Possamaï, 2018. "Moral Hazard Under Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 452-500, November.
    6. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2017. "Bank monitoring incentives under moral hazard and adverse selection," Working Papers hal-01435460, HAL.
    7. Sarah Bensalem & Nicolás Hernández-Santibáñez & Nabil Kazi-Tani, 2023. "A continuous-time model of self-protection," Finance and Stochastics, Springer, vol. 27(2), pages 503-537, April.
    8. Tianyu Ma & Zhuofu Wang & Jiyong Ding, 2018. "Governing the Moral Hazard in China’s Sponge City Projects: A Managerial Analysis of the Construction in the Non-Public Land," Sustainability, MDPI, vol. 10(9), pages 1-15, August.
    9. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.
    10. 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 Jan 2019.
    11. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 1-43, June.

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    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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