A Radner-Shepp model for an insurance company value is considered. The value is modelled as a Brownian motion with drift minus the dividend flow. The dividend flow plays the role of a control and the total discounted payoff is maximized.
For the case of zero liquidation value, the optimal dividend policy was determined by M. Jeanblanc and A. Shiryaev. In this presentaion, an explicit solution for the general case when the dissolution value is nonnegative is given. We treat separately three different kinds of admissible controls: continuous bounded rate dividend yield, discrete dividends with transaction costs, and a general non-negative, non-decreasing, right-continuous dividend flow.