Before revision:  In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding Hamilton-Jacobi-Bellman equation, which , in turn , leads to an optimal restricted dividend payment policy . When the claims are exponentially distributed, the value function and an optimal dividend payment policy of the threshold type are determined in closed forms under certain conditions. The case of unrestricted payment scheme gives rise to a singular stochastic control problem.
After revision:  In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding Hamilton-Jacobi-Bellman equation, which , in turn , leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme gives rise to a singular stochastic control problem.