  This paper studies an optimal stochastic impulse control problem in a finite
horizon with a decision lag, by which we mean that after an impulse is made, a
fixed number units of time has to be elapsed before the next impulse is allowed
to be made. The continuity of the value function is proved. A suitable version
of dynamic programming principle is established, which takes into account the
dependence of state process on the elapsed time. The corresponding
Hamilton-Jacobi-Bellman (HJB) equation is derived, which exhibit some special
feature of the problem. The value function of this optimal impulse control
problem is characterized as the unique viscosity solution to the corresponding
HJB equation. An optimal impulse control is constructed provided the value
function is given. Moreover, a limiting case with the waiting time approaching
$0$ is discussed.
