In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in , with optimal contracting between a competitive investor 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  how the maximization problem with implicit constraints faced by investors can be reduced to a classic stochastic control problem. The approach has the advantage of avoiding the more general techniques based on forward-backward stochastic differential equations described in  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.
Henri Pagès and Dylan Possamai
Classification JEL : G21, G28, G32
Keywords : Default Correlation, Dynamic Moral Hazard, Forward-Backward Stochastic Differential Equations.
Updated on: 06/12/2018 11:09