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In this paper, a characterization of the solution of impulse control problemsin terms of superharmonic functions is given. In a general Markovian framework,the value function of the impulse control problem is shown to be the minimalfunction in a convex set of superharmonic functions. This characterization alsoleads to optimal impulse control strategies and can be seen as thecorresponding characterization to the description of the value function foroptimal stopping problems as a smallest superharmonic majorant of the rewardfunction. The results are illustrated with examples from different fields,including multiple stopping and optimal switching problems.

On the Solution of General Impulse Control Problems Using Superharmonic Functions