  We study a finite horizon optimal contracting problem of a risk-neutral
principal and a risk-averse agent who receives a stochastic income stream when
the agent is unable to make commitments. The problem involves an infinite
number of constraints at each time and each state of the world. Miao and Zhang
(2015) have developed a dual approach to the problem by considering a
Lagrangian and derived a Hamilton-Jacobi-Bellman equation in an infinite
horizon. We consider a similar Lagrangian in a finite horizon, but transform
the dual problem into an infinite series of optimal stopping problems. For each
optimal stopping problem we provide an analytic solution by providing an
integral equation representation for the free boundary. We provide a
verification theorem that the value function of the original principal's
problem is the Legender-Fenchel transform of the integral of the value
functions of the optimal stopping problems. We also provide some numerical
simulation results of optimal contracting strategies
