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On Reflection with Two-Sided Jumps

Author

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  • Imane Jarni

    (Cadi Ayyad University)

  • Youssef Ouknine

    (Cadi Ayyad University
    Mohammed VI Polytechnic University)

Abstract

In the first part of this paper, we pose and solve a new version of Skorokhod problem with jumps, reflected in the half line $$\mathbb {R}^{+}$$ R + and associated to a right limited and left limited function. We show the existence and uniqueness of the solution for this problem. Then, we apply our result to prove existence and uniqueness of solutions of reflected stochastic differential equations driven by optional semimartingales on an unusual probability space.

Suggested Citation

  • Imane Jarni & Youssef Ouknine, 2021. "On Reflection with Two-Sided Jumps," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1811-1830, December.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:4:d:10.1007_s10959-020-01024-x
    DOI: 10.1007/s10959-020-01024-x
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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. Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
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