On the solution of general impulse control problems using superharmonic functions

Sören Christensen

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 709-729

Abstract: In this paper, a characterization of the solution of impulse control problems in terms of superharmonic functions is given. In a general Markovian framework, the value function of the impulse control problem is shown to be the minimal function in a convex set of superharmonic functions. This characterization also leads to optimal impulse control strategies and can be seen as the corresponding characterization to the description of the value function for optimal stopping problems as a smallest superharmonic majorant of the reward function. The results are illustrated with examples from different fields, including multiple stopping and optimal switching problems.

Keywords: Impulse control strategies; Superharmonic functions; General Markov processes (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (9)

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DOI: 10.1016/j.spa.2013.09.008

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