Choice of financing mode as a stochastic bounded control problem

In this note I analyze situations where an entrepreneur needs external financing from an outside investor in order to start an investment project that will yield a profit for two consecutive periods. The value of second-period profit is the entrepreneur's private information. I show that the choice of financing mode can be transformed into an optimal stochastic bounded control problem, where the state variable t represents the investor's first-period payoff and the control variable α can be interpreted in terms of the investor's residual profit rights. I then show that under certain general conditions such as the monotonicity and continuity of t (which have clear economic interpretations), an optimal contract is characterized by maximal α under low values of t and minimal α under high values of t. In economic terms this corresponds to debt.