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On reflected stochastic differential equations driven by regulated semimartingales

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  • Hilbert, Astrid
  • Jarni, Imane
  • Ouknine, Youssef

Abstract

We show the existence and uniqueness of the solutions of reflected stochastic differential equations driven by semimartingales with regulated trajectories. The study of these SDEs will be based on a new existence and uniqueness theorem for the deterministic Skorokhod problem when the driving process has only right and left limits.

Suggested Citation

  • Hilbert, Astrid & Jarni, Imane & Ouknine, Youssef, 2020. "On reflected stochastic differential equations driven by regulated semimartingales," Statistics & Probability Letters, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:stapro:v:167:y:2020:i:c:s0167715220302157
    DOI: 10.1016/j.spl.2020.108912
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    References listed on IDEAS

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    1. Abdelghani, Mohamed N. & Melnikov, Alexander V., 2017. "On linear stochastic equations of optional semimartingales and their applications," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 207-214.
    2. Slominski, Leszek & Wojciechowski, Tomasz, 2010. "Stochastic differential equations with jump reflection at time-dependent barriers," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1701-1721, August.
    3. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2017. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Post-Print hal-01141801, HAL.
    4. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    5. Kella, Offer, 2006. "Reflecting thoughts," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1808-1811, October.
    Full references (including those not matched with items on IDEAS)

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