| Abstract: |
In this paper, we take up the analysis of a principal/agent model with moral
hazard introduced in \cite{pages}, 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 \cite{san} 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 \cite{cviz} 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. |