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A mathematical treatment of bank monitoring incentives

Possamaï, Dylan; Pagès, Henri (2014), A mathematical treatment of bank monitoring incentives, Finance and Stochastics, 18, 1, p. 39-73. http://dx.doi.org/10.1007/s00780-013-0202-y

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1202.2076
Date
2014
Journal name
Finance and Stochastics
Volume
18
Number
1
Publisher
Springer
Pages
39-73
Publication identifier
http://dx.doi.org/10.1007/s00780-013-0202-y
Metadata
Show full item record
Author(s)
Possamaï, Dylan
Pagès, Henri
Abstract (EN)
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.
Subjects / Keywords
Verification theorem; Stochastic control; Optimal securitization; Optimal incentives; Dynamic moral hazard; Principal/agent problem
JEL
G32 - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
G28 - Government Policy and Regulation
G21 - Banks; Depository Institutions; Micro Finance Institutions; Mortgages

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