  We study the optimal financing and dividend distribution problem with
restricted dividend rates in a diffusion type surplus model where the drift and
volatility coefficients are general functions of the level of surplus and the
external environment regime. The environment regime is modeled by a Markov
process. Both capital injections and dividend payments incur expenses. The
objective is to maximize the expectation of the total discounted dividends
minus the total cost of capital injections. We prove that it is optimal to
inject capitals only when the surplus tends to fall below zero and to pay out
dividends at the maximal rate when the surplus is at or above the threshold
dependent on the environment regime.
