IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v144y2022icp1-22.html
   My bibliography  Save this article

Strong solutions of forward–backward stochastic differential equations with measurable coefficients

Author

Listed:
  • Luo, Peng
  • Menoukeu-Pamen, Olivier
  • Tangpi, Ludovic

Abstract

This paper investigates solvability of fully coupled systems of forward–backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to construct strong solutions. Despite the irregularity of the coefficients, the solutions turn out to be differentiable, at least in the Malliavin sense and, as functions of the initial variable, in the Sobolev sense.

Suggested Citation

  • Luo, Peng & Menoukeu-Pamen, Olivier & Tangpi, Ludovic, 2022. "Strong solutions of forward–backward stochastic differential equations with measurable coefficients," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 1-22.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:1-22
    DOI: 10.1016/j.spa.2021.10.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414921001812
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.10.012?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. Issoglio, Elena & Jing, Shuai, 2020. "Forward–backward SDEs with distributional coefficients," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 47-78.
    2. 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.
    3. 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.
    4. Antonelli, Fabio & Hamadène, SaI¨d, 2006. "Existence of the solutions of backward-forward SDE's with continuous monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1559-1569, August.
    5. 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.
    6. 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.
    7. 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.
    8. Gregor Heyne & Michael Kupper & Ludovic Tangpi, 2016. "Portfolio Optimization Under Nonlinear Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    9. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
    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. Olivier Menoukeu-Pamen & Ludovic Tangpi, 2023. "Maximum Principle for Stochastic Control of SDEs with Measurable Drifts," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1195-1228, June.

    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. 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.
    2. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    3. Yushi Hamaguchi, 2019. "Time-inconsistent consumption-investment problems in incomplete markets under general discount functions," Papers 1912.01281, arXiv.org, revised Mar 2021.
    4. 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.
    5. Barrasso, Adrien & Russo, Francesco, 2021. "Martingale driven BSDEs, PDEs and other related deterministic problems," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 193-228.
    6. Adrien Barrasso & Francesco Russo, 2021. "Backward Stochastic Differential Equations with No Driving Martingale, Markov Processes and Associated Pseudo-Partial Differential Equations: Part II—Decoupled Mild Solutions and Examples," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1110-1148, September.
    7. Martin Herdegen & Johannes Muhle-Karbe & Dylan Possamai, 2019. "Equilibrium Asset Pricing with Transaction Costs," Papers 1901.10989, arXiv.org, revised Sep 2020.
    8. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    9. Brigo, Damiano & Francischello, Marco & Pallavicini, Andrea, 2019. "Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement," European Journal of Operational Research, Elsevier, vol. 274(2), pages 788-805.
    10. Olivier Menoukeu-Pamen & Ludovic Tangpi, 2023. "Maximum Principle for Stochastic Control of SDEs with Measurable Drifts," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1195-1228, June.
    11. Daniel Bartl & Ariel Neufeld & Kyunghyun Park, 2023. "Sensitivity of robust optimization problems under drift and volatility uncertainty," Papers 2311.11248, arXiv.org.
    12. 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.
    13. Li, Juan & Wei, Qingmeng, 2014. "Lp estimates for fully coupled FBSDEs with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1582-1611.
    14. Kraft, Holger & Seiferling, Thomas & Seifried, Frank Thomas, 2016. "Optimal consumption and investment with Epstein-Zin recursive utility," SAFE Working Paper Series 52, Leibniz Institute for Financial Research SAFE, revised 2016.
    15. Gobet, Emmanuel & Makhlouf, Azmi, 2010. "-time regularity of BSDEs with irregular terminal functions," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1105-1132, July.
    16. Issoglio, Elena & Jing, Shuai, 2020. "Forward–backward SDEs with distributional coefficients," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 47-78.
    17. Kihun Nam, 2019. "Global Well-posedness of Non-Markovian Multidimensional Superquadratic BSDE," Papers 1912.03692, arXiv.org, revised Jan 2022.
    18. Popier, A., 2006. "Backward stochastic differential equations with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 2014-2056, December.
    19. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    20. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.

    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:144:y:2022:i:c:p:1-22. 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.