A mathematical treatment of bank monitoring incentives
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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|Date of creation:||2014|
|Date of revision:|
|Publication status:||Published in Finance and Stochastics, 2014, Vol. 18, no. 1. pp. 39-73.Length: 34 pages|
|Contact details of provider:|| Web page: http://www.dauphine.fr/en/welcome.html|
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