A Continuous-Time Principal-Agent Model with Privately Observable Cash Flows. Preliminary and Incomplete

We consider a principal-agent model, in which the agent needs to borrow from the principal to finance a project. Our model is based on DeMarzo and Fishman (2003), except that the agent’s cash flows are given by a Brownian motion with drift in continuous time. The difficulty in writing an appropriate financial contract in this setting lies in the fact that the agent can hide cash flows and not pay back the principal. To enforce payments, the principal has the ability to terminate the agent’s project. We design a new way to analyze the problem of private information in continuous time. Using techniques from stochastic calculus, we characterize the optimal contract by a differential equation. We show that this contract is equivalent to the limiting case of a discrete time model with binomial cash flows. The optimal contract can be interpreted as a combination of equity, a credit line, and either longterm debt or a compensating balance requirement (i.e., a cash position). The project is terminated if the agent defaults on the debt or exceeds the limit on the credit line. Once the credit line is paid off, excess cash flows are used to pay dividends. The agent is compensated with equity alone. Unlike the discrete time setting, our differential equation for the continuous time model allows us to compute contracts easily, as well as compute comparative statics. Currently, we are working on a number of extensions to the basic model.