IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i9p2881-2912.html
   My bibliography  Save this article

BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game

Author

Listed:
  • Hamadène, S.
  • Wang, H.

Abstract

In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limit obstacles (or barriers) when the noise is given by Brownian motion and a mutually independent Poisson random measure. The jumps of the obstacle processes could be either predictable or inaccessible. We show the existence and uniqueness of the solution when the barriers are completely separated and the generator uniformly Lipschitz. We do not assume the existence of a difference of supermartingales between the obstacles. As an application, we show that the related mixed zero-sum differential-integral game problem has a value.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:9:p:2881-2912
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00058-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tomasz R. Bielecki & Stéphane Crépey & Monique Jeanblanc & Marek Rutkowski, 2008. "Defaultable Options In A Markovian Intensity Model Of Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 493-518, October.
    2. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    4. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    5. Bahlali, Khaled & Hamadène, SaI¨d & Mezerdi, Brahim, 2005. "Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1107-1129, July.
    6. 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.
    7. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    8. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    9. Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Monia Karouf, 2019. "Reflected and Doubly Reflected Backward Stochastic Differential Equations with Time-Delayed Generators," Journal of Theoretical Probability, Springer, vol. 32(1), pages 216-248, March.
    2. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    3. Eddahbi, M’hamed & Fakhouri, Imade & Ouknine, Youssef, 2020. "Reflected BSDEs with jumps in time-dependent convex càdlàg domains," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6515-6555.
    4. Klimsiak, Tomasz, 2015. "Reflected BSDEs on filtered probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4204-4241.
    5. 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.
    6. 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.

    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. Erhan Bayraktar & Song Yao, 2015. "On the Robust Dynkin Game," Papers 1506.09184, arXiv.org, revised Sep 2016.
    2. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    3. 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.
    4. 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.
    5. Bahlali, Khaled & Hamadène, SaI¨d & Mezerdi, Brahim, 2005. "Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1107-1129, July.
    6. Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
    7. Zhou Zhou, 2015. "Non-zero-sum stopping games in discrete time," Papers 1508.06032, arXiv.org.
    8. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.
    9. Zhou, Qing & Ren, Yong, 2012. "Reflected backward stochastic differential equations with time delayed generators," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 979-990.
    10. Said Hamadene & Jianfeng Zhang, 2008. "The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options," Papers 0810.5698, arXiv.org.
    11. Guo, Ivan & Rutkowski, Marek, 2016. "Discrete time stochastic multi-player competitive games with affine payoffs," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 1-32.
    12. Djordjević, Jasmina & Janković, Svetlana, 2015. "Backward stochastic Volterra integral equations with additive perturbations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 903-910.
    13. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    14. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    15. Miryana Grigorova & Marie-Claire Quenez & Yuan Peng, 2023. "Non-linear non-zero-sum Dynkin games with Bermudan strategies," Papers 2311.01086, arXiv.org.
    16. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    17. Joffrey Derchu & Philippe Guillot & Thibaut Mastrolia & Mathieu Rosenbaum, 2020. "AHEAD : Ad-Hoc Electronic Auction Design," Papers 2010.02827, arXiv.org.
    18. Giovanni Mottola, 2014. "Generalized Dynkin game of switching type representation for defaultable claims in presence of contingent CSA," Papers 1410.0594, arXiv.org, revised Jan 2015.
    19. Hsuan-Ku Liu, 2013. "The pricing formula for cancellable European options," Papers 1304.5962, arXiv.org, revised Sep 2014.
    20. Hamadène, Said & Mu, Rui, 2020. "Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6901-6926.

    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:119:y:2009:i:9:p:2881-2912. 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.