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

A Finite Horizon Optimal Stochastic Impulse Control Problem with A Decision Lag