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A mathematical treatment of bank monitoring incentives

Henri Pag\`es and Dylan Possama\"i
Authors registered in the RePEc Author Service: Henri F. Pagès ()

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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.

Date: 2012-02, Revised 2015-04
New Economics Papers: this item is included in nep-ban, nep-bec, nep-cta, nep-mic and nep-mon
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Related works:
Journal Article: A mathematical treatment of bank monitoring incentives (2014) Downloads
Working Paper: A mathematical treatment of bank monitoring incentives (2012) Downloads
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