  Consider an insurance company for which the reserve process follows the
Sparre Anderson model. In this paper, we study the optimal dividend problem for
such a company as Bai, Ma and Xing [9] do. However, we remove the constant
restriction on the dividend rates, i.e. the optimization problem is of singular
type. In this case, the value function is no longer bounded and the associated
HJB equation is a variational inequality involving a first order
integro-differential operator and a gradient constraint. We use other
techniques to prove the regularity properties for the value function and show
that the value function is a constrained viscosity solution of the associated
HJB equation. In addition, we show that the value function is the upper
semi-continuous envelop of the supremum for a class of subsolutions.
