IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i8p2583-2604.html
   My bibliography  Save this article

Solvability of forward–backward stochastic partial differential equations

Author

Listed:
  • Yin, Hong

Abstract

In this paper we study the solvability of a class of fully-coupled forward–backward stochastic partial differential equations (FBSPDEs). These FBSPDEs cannot be put into the framework of stochastic evolution equations in general, and the usual decoupling methods for the Markovian forward–backward SDEs are difficult to apply. We prove the well-posedness of the FBSPDEs, under various conditions on the coefficients, by using either the method of contraction mapping or the method of continuation. These conditions, especially in the higher dimensional case, are novel in the literature.

Suggested Citation

  • Yin, Hong, 2014. "Solvability of forward–backward stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2583-2604.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2583-2604
    DOI: 10.1016/j.spa.2014.03.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914000568
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.03.005?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. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    2. Ma, Jin & Yong, Jiongmin, 1997. "Adapted solution of a degenerate backward spde, with applications," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 59-84, October.
    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. Bo Yan & Yanping Liu & Si Liu, 2023. "Corporate social responsibility in long‐term supply chain management," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(1), pages 17-27, January.

    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. Ma, Jin & Yin, Hong & Zhang, Jianfeng, 2012. "On non-Markovian forward–backward SDEs and backward stochastic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3980-4004.
    2. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    3. Menozzi, Stéphane, 2018. "Martingale problems for some degenerate Kolmogorov equations," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 756-802.
    4. Umut c{C}etin & Albina Danilova, 2014. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," Papers 1407.2420, arXiv.org, revised Sep 2016.
    5. Masaaki Fujii, 2020. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-497, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    7. Arvind V. Shrivats & Dena Firoozi & Sebastian Jaimungal, 2022. "A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 779-824, July.
    8. Confortola, Fulvia, 2007. "Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 613-628, May.
    9. Masaaki Fujii, 2019. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CIRJE F-Series CIRJE-F-1133, CIRJE, Faculty of Economics, University of Tokyo.
    10. Delbaen, Freddy & Qiu, Jinniao & Tang, Shanjian, 2015. "Forward–backward stochastic differential systems associated to Navier–Stokes equations in the whole space," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2516-2561.
    11. Englezos, Nikolaos & Frangos, Nikolaos E. & Kartala, Xanthi-Isidora & Yannacopoulos, Athanasios N., 2013. "Stochastic Burgers PDEs with random coefficients and a generalization of the Cole–Hopf transformation," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3239-3272.
    12. Anne Eyraud-Loisel, 2013. "Quadratic hedging in an incomplete market derived by an influent informed investor," Post-Print hal-00450949, HAL.
    13. J. T. Shi & Z. Wu, 2010. "Maximum Principle for Partially-Observed Optimal Control of Fully-Coupled Forward-Backward Stochastic Systems," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 543-578, June.
    14. Mikami, Toshio & Thieullen, Michèle, 2006. "Duality theorem for the stochastic optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1815-1835, December.
    15. Delarue, F. & Guatteri, G., 2006. "Weak existence and uniqueness for forward-backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1712-1742, December.
    16. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    17. Rene Carmona & Francois Delarue & Gilles-Edouard Espinosa & Nizar Touzi, 2012. "Singular Forward-Backward Stochastic Differential Equations and Emissions Derivatives," Papers 1210.5773, arXiv.org.
    18. Delarue, François & Foguen Tchuendom, Rinel, 2020. "Selection of equilibria in a linear quadratic mean-field game," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1000-1040.
    19. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2014. "Forward–backward systems for expected utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1813-1848.
    20. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2018. "Equilibrium Returns with Transaction Costs," Post-Print hal-01569408, HAL.

    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:124:y:2014:i:8:p:2583-2604. 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.