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

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  • Goldys, Beniamin
  • Wu, Wei

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).

Suggested Citation

  • Goldys, Beniamin & Wu, Wei, 2019. "On a class of singular stochastic control problems driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3174-3206.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3174-3206
    DOI: 10.1016/j.spa.2018.09.002
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    References listed on IDEAS

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    1. Takashi Kato, 2009. "An Optimal Execution Problem with Market Impact," Papers 0907.3282, arXiv.org, revised Dec 2014.
    2. Takashi Kato, 2014. "An optimal execution problem with market impact," Finance and Stochastics, Springer, vol. 18(3), pages 695-732, July.
    3. Ishikawa, Yasushi & Kunita, Hiroshi, 2006. "Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1743-1769, December.
    4. Giulia Di Nunno & Thilo Meyer-Brandis & Bernt Øksendal & Frank Proske, 2006. "Optimal portfolio for an insider in a market driven by Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 83-94.
    5. Takashi Kato, 2011. "An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process," Papers 1107.1787, arXiv.org, revised Jul 2014.
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