Dividend Optimization for a Regime-Switching Diffusion Model with Restricted Dividend Rates

We consider the optimal dividend control problem to find an optimal strategy under the constraint that dividend rates are restricted such that the expected total discounted dividends is maximized for an insurance company. The evolution of the reserve is modeled by a diffusion process with drift and volatility coefficients modulated by an observable Markov chain. We consider the regime-switching threshold strategy, which pays out dividends at the maximal possible rate when the current reserve is above some critical level dependent on the regime of the Markov chain at the time, and to pay nothing when the reserve is below that level. We give sufficient conditions under which such type of strategy is optimal for the regime-switching model