On a class of singular stochastic control problems driven by Lévy noise

Beniamin Goldys and Wei Wu

Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3174-3206

Abstract: A class of singular stochastic control problems whose value functions satisfy an invariance property was studied by Lasry and Lions (2000). They have shown that, within this class, any singular control problem is equivalent to the corresponding standard stochastic control problem. The equivalence is in the sense that their value functions are equal. In this work, we clarify their idea and extend their work to allow Lévy type noise. In addition, for the purpose of application, we apply our result to an optimal trade execution problem studied by Lasry and Lions (2007).

Keywords: Singular stochastic control problems; Lévy noise; Invariance; Optimal trade executions (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.09.002

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