Optimal Dividend Control in Presence of Downside Risk

We analyze the determination of a value maximizing dividend policy for a broad class of cash flow processes modelled as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the value of the optimal dividend policy explicitly. Utilizing this result, we also characterize explicitly the values as well as the optimal dividend thresholds for a class of associated optimal stopping and sequential impulse control problems. Our results indicate that both the value as well as the marginal value of the optimal policy are increasing functions of policy flexibility in the discontinuous setting as well.