IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v167y2020ics0167715220302157.html
   My bibliography  Save this article

On reflected stochastic differential equations driven by regulated semimartingales

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220302157
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108912?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Imane Jarni & Youssef Ouknine, 2021. "On Reflection with Two-Sided Jumps," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1811-1830, December.
    2. Klimsiak, Tomasz, 2021. "Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 208-239.
    3. Ihsan Arharas & Siham Bouhadou & Youssef Ouknine, 2022. "Doubly Reflected Backward Stochastic Differential Equations in the Predictable Setting," Journal of Theoretical Probability, Springer, vol. 35(1), pages 115-141, March.
    4. Marzougue, Mohamed, 2020. "A note on optional Snell envelopes and reflected backward SDEs," Statistics & Probability Letters, Elsevier, vol. 165(C).
    5. Grigorova, Miryana & Quenez, Marie-Claire & Sulem, Agnès, 2021. "American options in a non-linear incomplete market model with default," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 479-512.
    6. Grigorova, Miryana & Imkeller, Peter & Ouknine, Youssef & Quenez, Marie-Claire, 2020. "Optimal stopping with f-expectations: The irregular case," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1258-1288.
    7. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2020. "European options in a non-linear incomplete market model with default," Post-Print hal-02025833, HAL.
    8. Grigorova, Miryana & Quenez, Marie-Claire & Sulem, Agnès, 2019. "Superhedging prices of European and American options in a non-linear incomplete market with default," Center for Mathematical Economics Working Papers 607, Center for Mathematical Economics, Bielefeld University.
    9. Hanwu Li & Guomin Liu, 2024. "Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2615-2645, September.
    10. Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Vulnerable European and American Options in a Market Model with Optional Hazard Process," Papers 2212.12860, arXiv.org.
    11. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "American options in a non-linear incomplete market model with default," Working Papers hal-02025835, HAL.
    12. Marzougue, Mohamed, 2021. "Monotonic limit theorem for BSDEs with regulated trajectories," Statistics & Probability Letters, Elsevier, vol. 176(C).
    13. Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs," Papers 2212.12854, arXiv.org.
    14. Abdelkarim Oualaid & Khaled Bahlali & Youssef Ouknine, 2023. "Reflected Backward Stochastic Differential Equations Associated to Jump Markov Processes and Application to Partial Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1400-1436, September.
    15. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "European options in a non-linear incomplete market model with default," Working Papers hal-02025833, HAL.
    16. Li, Hanwu, 2024. "Backward stochastic differential equations with double mean reflections," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    17. Ivanovs, Jevgenijs & Boxma, Onno, 2015. "A bivariate risk model with mutual deficit coverage," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 126-134.
    18. Dumitrescu, Roxana & Elie, Romuald & Sabbagh, Wissal & Zhou, Chao, 2023. "A new Mertens decomposition of Yg,ξ-submartingale systems. Application to BSDEs with weak constraints at stopping times," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 183-205.
    19. Thomas Kruse & Philipp Strack, 2019. "An Inverse Optimal Stopping Problem for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 423-439, May.
    20. Falkowski, Adrian & Słomiński, Leszek, 2022. "SDEs with two reflecting barriers driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 164-186.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:167:y:2020:i:c:s0167715220302157. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.