Optimal ratcheting dividend policies with resets

We study an optimal dividend policy problem under ratcheting and bankruptcy constraints. Firms face a tradeoff between the negative signal of a dividend reduction and a potential future bankruptcy. In contrast to previous works, the dividend rate is allowed to decrease after incurring a negative impact on equity valuation in accordance with a large empirical literature on the topic. We provide an explicit necessary and sufficient condition for the finiteness of the value function and prove the differentiability of the value function, and its characterization via viscosity solutions and the so-called supercontact property. The value function is given by the solution of a two-dimensional variational inequality combining optimal stopping, singular and impulse controls. We show that the problem is equivalent to a one-dimensional setup simplifying both mathematical and financial analysis. Finally, we provide a numerical study of the model and a sensitivity analysis with respect to the model parameters. We show the relevance of over-reaction to financial news on the manager's optimal policy.