Optimal financing of a corporation subject to random returns: a summary

We address the problem of finding an optimal financing mix of retained earnings and external equity for maximizing the value of a firm subject to random returns. The problem is formulated as a singular stochastic control for a diffusion process, and the value function satisfies a free-boundary problem. The optimal policy can be characterized in terms of two threshold levels for the asset level. Below the lower threshold, the optimal policy is to retain all earnings and raise the required external equity. Above the higher threshold, the optimal policy is to pay all earnings as dividends and to bring in no new equity. Between the two thresholds, the optimal policy is to retain all earnings but not raise any external equity. We provide economic interpretations of the optimal policy.