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On the solution of general impulse control problems using superharmonic functions

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  • Christensen, Sören

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.

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  • Christensen, Sören, 2014. "On the solution of general impulse control problems using superharmonic functions," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 709-729.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:709-729
    DOI: 10.1016/j.spa.2013.09.008
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    Cited by:

    1. Vicky Henderson & Jonathan Muscat, 2020. "Partial liquidation under reference-dependent preferences," Finance and Stochastics, Springer, vol. 24(2), pages 335-357, April.
    2. Mike Ludkovski, 2022. "Regression Monte Carlo for Impulse Control," Papers 2203.06539, arXiv.org.
    3. Christoph Belak & Lukas Mich & Frank T. Seifried, 2019. "Optimal Investment for Retail Investors with Flooredand Capped Costs," Working Paper Series 2019-06, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    4. Christoph Belak & Sören Christensen, 2019. "Utility maximisation in a factor model with constant and proportional transaction costs," Finance and Stochastics, Springer, vol. 23(1), pages 29-96, January.
    5. Soren Christensen & Berenice Anne Neumann & Tobias Sohr, 2020. "Competition versus Cooperation: A class of solvable mean field impulse control problems," Papers 2010.06452, arXiv.org, revised Apr 2021.
    6. Christensen, Sören & Sohr, Tobias, 2020. "A solution technique for Lévy driven long term average impulse control problems," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7303-7337.
    7. Christoph Belak & Lukas Mich & Frank T. Seifried, 2022. "Optimal investment for retail investors," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 555-594, April.
    8. Christoph Belak & Jörn Sass, 2019. "Finite-horizon optimal investment with transaction costs: construction of the optimal strategies," Finance and Stochastics, Springer, vol. 23(4), pages 861-888, October.
    9. Szabó, Dávid Zoltán & Duck, Peter & Johnson, Paul, 2020. "Optimal trading of imbalance options for power systems using an energy storage device," European Journal of Operational Research, Elsevier, vol. 285(1), pages 3-22.

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