Optimal firm’s dividend and capital structure with mean reverting profitability

We model a risk-averse decision maker who maximizes the inter-temporal expected utility of a firm's dividend payouts, choosing both dividends and leverage. The firm's value and profitability are both stochastic state variables. Motivated by empirical evidence, we model profitability using a mean reverting process. The problem has a quasi-explicit solution. When calibrating the model to actual U.S. data, we show that the optimal dividend policy is smooth and that leverage is, on average, stable over time, in line with empirical evidence. We highlight that these results are related to the strength of profitability’ s mean reversion without the need to account for either asymmetric information or other frictions.