IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v155y2019ic1.html
   My bibliography  Save this article

Transportation cost inequality for backward stochastic differential equations

Author

Listed:
  • Bahlali, Khaled
  • Boufoussi, Brahim
  • Mouchtabih, Soufiane

Abstract

We prove that probability laws of a backward stochastic differential equation, satisfy a quadratic transportation cost inequality under the uniform metric. That is, a comparison of the Wasserstein distance from the law of the solution of the equation to any other absolutely continuous measure with finite relative entropy. From this we derive concentration properties of Lipschitz functions of the solution.

Suggested Citation

  • Bahlali, Khaled & Boufoussi, Brahim & Mouchtabih, Soufiane, 2019. "Transportation cost inequality for backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:155:y:2019:i:c:1
    DOI: 10.1016/j.spl.2019.108586
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219302329
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.108586?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. Daniel Lacker, 2018. "Liquidity, Risk Measures, and Concentration of Measure," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 813-837, August.
    3. Ludovic Tangpi, 2018. "Concentration of dynamic risk measures in a Brownian filtration," Papers 1805.09014, arXiv.org.
    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. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).

    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. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2011. "Forward-backward systems for expected utility maximization," SFB 649 Discussion Papers 2011-061, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    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, 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Yin, Hong, 2014. "Solvability of forward–backward stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2583-2604.
    11. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2022. "Star-Shaped deviations," Papers 2207.08613, arXiv.org.
    12. 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.
    13. Martin Herdegen & Johannes Muhle-Karbe & Dylan Possamai, 2019. "Equilibrium Asset Pricing with Transaction Costs," Papers 1901.10989, arXiv.org, revised Sep 2020.
    14. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2021. "Deep Learning Algorithms for Hedging with Frictions," Papers 2111.01931, arXiv.org, revised Dec 2022.
    15. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).
    16. Masaaki Fujii, 2019. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-467, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2017. "Equilibrium Returns with Transaction Costs," Papers 1707.08464, arXiv.org, revised Apr 2018.
    18. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    19. 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.
    20. Anne Eyraud-Loisel, 2011. "Option Hedging By An Influent Informed Investor," Post-Print hal-00450948, 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:stapro:v:155:y:2019:i:c:1. 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.