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 publiéExternal document link
http://arxiv.org/abs/1202.2076Date
2014Journal name
Finance and StochasticsVolume
18Number
1Publisher
Springer
Pages
39-73
Publication identifier
Metadata
Show full item recordAbstract (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 problemRelated items
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