Dividend Optimization for Regime Switching General Diffusions

We consider the optimal dividend distribution problem of a financial corporation whose surplus is modeled by a general diffusion process with both the drift and the diffusion coefficients depending on the external economic regime as well as the surplus itself through general functions. The aim is to find a dividend payout scheme that maximizes the present value of the total dividends until ruin. We show that, depending on the configuration of the model parameters, there are two exclusive scenarios: (i) the optimal strategy uniquely exists and corresponds to paying out all surplus in excess of a critical level (barrier) dependent on the economic regime and paying nothing when the surplus is below the critical level; and (ii) there are no optimal strategies