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
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1202.2076
Journal nameFinance and Stochastics
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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 / KeywordsVerification theorem; Stochastic control; Optimal securitization; Optimal incentives; Dynamic moral hazard; Principal/agent problem
Showing items related by title and author.
Bouchard, Bruno; Possamaï, Dylan; Tan, Xiaolu; Zhou, Chao (2017) Article accepté pour publication ou publié