IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i6p1588-1594.html
   My bibliography  Save this article

The Lp Cauchy sequence for one-dimensional BSDEs with linear growth generators

Author

Listed:
  • Izumi, Yuki

Abstract

In this paper, the existence of Lp(p>1) solutions for one-dimensional backward stochastic differential equations will be shown directly by proving that an approximation sequence is a Cauchy one in the Lp sense.

Suggested Citation

  • Izumi, Yuki, 2013. "The Lp Cauchy sequence for one-dimensional BSDEs with linear growth generators," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1588-1594.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:6:p:1588-1594
    DOI: 10.1016/j.spl.2013.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213000795
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.03.006?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. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    2. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    3. 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.
    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. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    2. Fan, ShengJun, 2016. "Bounded solutions, Lp(p>1) solutions and L1 solutions for one dimensional BSDEs under general assumptions," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1511-1552.
    3. Fan, Shengjun & Hu, Ying, 2021. "Well-posedness of scalar BSDEs with sub-quadratic generators and related PDEs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 21-50.
    4. Fan, ShengJun & Jiang, Long & Tian, DeJian, 2011. "One-dimensional BSDEs with finite and infinite time horizons," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 427-440, March.
    5. Sheng-Jun Fan & Long Jiang, 2012. "A Generalized Comparison Theorem for BSDEs and Its Applications," Journal of Theoretical Probability, Springer, vol. 25(1), pages 50-61, March.
    6. Zhang, HengMin & Fan, ShengJun, 2013. "A representation theorem for generators of BSDEs with finite or infinite time intervals and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 724-734.
    7. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.
    8. Fan, Shengjun & Hu, Ying & Tang, Shanjian, 2023. "Existence, uniqueness and comparison theorem on unbounded solutions of scalar super-linear BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 335-375.
    9. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
    10. Cao, Guilan & He, Kai, 2007. "Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1251-1264, September.
    11. Sheng Jun Fan, 2018. "Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1860-1899, September.
    12. Graewe, Paulwin & Popier, Alexandre, 2021. "Asymptotic approach for backward stochastic differential equation with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 247-277.
    13. 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.
    14. Kruse, T. & Popier, A., 2016. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2554-2592.
    15. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
    16. Xing, Hao, 2012. "On backward stochastic differential equations and strict local martingales," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2265-2291.
    17. Fan, ShengJun & Jiang, Long, 2012. "One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1792-1798.
    18. Mingyu Xu & Zuo Quan Xu & Xun Yu Zhou, 2022. "$g$-Expectation of Distributions," Papers 2208.06535, arXiv.org.
    19. Tian, Dejian & Jiang, Long & Davison, Matt, 2010. "On the existence of solutions to BSDEs with generalized uniformly continuous generators," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 903-909, May.
    20. Bayraktar, Erhan & Yao, Song, 2012. "Quadratic reflected BSDEs with unbounded obstacles," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1155-1203.

    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:83:y:2013:i:6:p:1588-1594. 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.