A mathematical treatment of bank monitoring incentives

作者：Pages Henri; Possamai Dylan^*

来源：Finance and Stochastics, 2014, 18(1): 39-73.

DOI：10.1007/s00780-013-0202-y

• Principal/agent problem
• Dynamic moral hazard
• Optimal incentives
• Optimal securitization
• Stochastic control
• Verification theorem

In this paper, we take up the analysis of a principal/agent model with moral hazard introduced by Pages (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 Cvitanic 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.

• 出版日期2014-1