IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v134y2021icp208-239.html
   My bibliography  Save this article

Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games

Author

Listed:
  • Klimsiak, Tomasz

Abstract

We introduce a new class of reflected backward stochastic differential equations with two càdlàg barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove existence, uniqueness and approximation results for solutions of equations defined on general filtered probability spaces. Applications to nonlinear Dynkin games are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:134:y:2021:i:c:p:208-239
    DOI: 10.1016/j.spa.2020.12.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414920304385
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.12.008?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. Klimsiak, Tomasz, 2015. "Reflected BSDEs on filtered probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4204-4241.
    2. Bayraktar, Erhan & Yao, Song, 2015. "Doubly reflected BSDEs with integrable parameters and related Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4489-4542.
    3. Quenez, Marie-Claire & Sulem, Agnès, 2014. "Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3031-3054.
    4. Hamadène, S. & Wang, H., 2009. "BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2881-2912, September.
    5. Hamadène, S. & Lepeltier, J. -P., 2000. "Reflected BSDEs and mixed game problem," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 177-188, February.
    6. 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.
    7. Klimsiak, Tomasz, 2019. "Systems of quasi-variational inequalities related to the switching problem," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1259-1286.
    8. Lin, Qian, 2015. "Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4405-4454.
    9. Rozkosz, Andrzej & Słomiński, Leszek, 2012. "Lp solutions of reflected BSDEs under monotonicity condition," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3875-3900.
    10. Miryana Grigorova & Peter Imkeller & Youssef Ouknine & Marie-Claire Quenez, 2018. "Doubly Reflected BSDEs and ${\cal E}^{f}$-Dynkin games: beyond the right-continuous case," Working Papers hal-01497914, HAL.
    11. 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.
    12. Grigorova, Miryana & Imkeller, Peter & Quenez, Marie-Claire & Ouknine, Youssef, 2018. "Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case," Center for Mathematical Economics Working Papers 598, Center for Mathematical Economics, Bielefeld University.
    13. Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
    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. Marzougue, Mohamed, 2020. "A note on optional Snell envelopes and reflected backward SDEs," Statistics & Probability Letters, Elsevier, vol. 165(C).
    2. 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.
    3. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "European options in a non-linear incomplete market model with default," Working Papers hal-02025833, HAL.
    4. 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.
    5. Kim, Mun-Chol & O, Hun, 2021. "A general comparison theorem for reflected BSDEs," Statistics & Probability Letters, Elsevier, vol. 173(C).
    6. Marzougue, Mohamed, 2021. "Monotonic limit theorem for BSDEs with regulated trajectories," Statistics & Probability Letters, Elsevier, vol. 176(C).
    7. 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.
    8. Imane Jarni & Youssef Ouknine, 2021. "On Reflection with Two-Sided Jumps," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1811-1830, December.
    9. Tianyang Nie & Edward Kim & Marek Rutkowski, 2018. "Arbitrage-Free Pricing of Game Options in Nonlinear Markets," Papers 1807.05448, arXiv.org.
    10. 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.
    11. 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.
    12. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "American options in a non-linear incomplete market model with default," Working Papers hal-02025835, HAL.
    13. Fan, Xiliang & Ren, Yong & Zhu, Dongjin, 2010. "A note on the doubly reflected backward stochastic differential equations driven by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 690-696, April.
    14. 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.
    15. Erhan Bayraktar & Song Yao, 2015. "On the Robust Dynkin Game," Papers 1506.09184, arXiv.org, revised Sep 2016.
    16. Klimsiak, Tomasz, 2015. "Reflected BSDEs on filtered probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4204-4241.
    17. Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs," Papers 2212.12854, arXiv.org.
    18. 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.
    19. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2015. "Game options in an imperfect market with default," Papers 1511.09041, arXiv.org, revised Jul 2017.
    20. Bensoussan, Alain & Li, Yiqun & Yam, Sheung Chi Phillip, 2018. "Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 644-688.

    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:spapps:v:134:y:2021:i:c:p:208-239. 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/505572/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.