IDEAS home Printed from https://ideas.repec.org/p/ajf/louvlf/2025001.html

On the distribution of the integral of a function with respect to a Brownian Bridge

Author

Listed:
  • Vrins, Frédéric

    (Université catholique de Louvain, LIDAM/LFIN, Belgium)

Abstract

We derive a couple of results associated with the distribution of the integral J of a square-integrable function with respect to a Brownian bridge. These results are useful to design sampling algorithms and provide a tight upper bound for the distribution of the running supremum of J.

Suggested Citation

  • Vrins, Frédéric, 2025. "On the distribution of the integral of a function with respect to a Brownian Bridge," LIDAM Discussion Papers LFIN 2025001, Université catholique de Louvain, Louvain Finance (LFIN).
    • Handle: RePEc:ajf:louvlf:2025001
    as

    Download full text from publisher

    File URL: https://dial.uclouvain.be/pr/boreal/en/object/boreal%3A300172/datastream/PDF_01/view
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Monique Jeanblanc & Frédéric Vrins, 2018. "Conic martingales from stochastic integrals," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 516-535, April.
    2. Damiano Brigo & Fabio Mercurio, 2006. "Interest Rate Models — Theory and Practice," Springer Finance, Springer, edition 0, number 978-3-540-34604-3, March.
    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. Vrins, Frédéric, 2026. "Joint pricing of default-free and defaultable claims in a reduced-form model featuring a martingale part," European Journal of Operational Research, Elsevier, vol. 329(1), pages 180-197.

    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. Vrins, Frédéric, 2026. "Joint pricing of default-free and defaultable claims in a reduced-form model featuring a martingale part," European Journal of Operational Research, Elsevier, vol. 329(1), pages 180-197.
    2. Cheikh Mbaye & Frédéric Vrins, 2018. "A Subordinated Cir Intensity Model With Application To Wrong-Way Risk Cva," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-22, November.
    3. Brigo, Damiano & Jeanblanc, Monique & Vrins, Frédéric, 2020. "SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3895-3919.
    4. Cheikh Mbaye & Frédéric Vrins, 2022. "Affine term structure models: A time‐change approach with perfect fit to market curves," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 678-724, April.
    5. Hainaut, Donatien, 2026. "American option pricing with model constrained Gaussian process regressions," Applied Mathematics and Computation, Elsevier, vol. 512(C).
    6. BRIGO, Damiano & VRINS, Frédéric, 2018. "Disentangling wrong-way risk: pricing credit valuation adjustment via change of measures," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1154-1164.
    7. Damiano Brigo & Fr'ed'eric Vrins, 2016. "Disentangling wrong-way risk: pricing CVA via change of measures and drift adjustment," Papers 1611.02877, arXiv.org.
    8. Stefano Scoleri & Marco Bianchetti & Sergei Kucherenko, 2026. "Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks," Papers 2602.14354, arXiv.org.
    9. Hainaut, Donatien, 2024. "American option pricing with model constrained Gaussian process regressions," LIDAM Discussion Papers ISBA 2024023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Chen, Shukai & Fang, Rongjuan & Ji, Lina & Wang, Jian, 2026. "Exponential ergodicity of CBIRE-processes with competition and catastrophes," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    11. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "An arbitrage-free conic martingale model with application to credit risk," Papers 1909.02474, arXiv.org.
    12. Frédéric Vrins, 2017. "Wrong-Way Risk Cva Models With Analytical Epe Profiles Under Gaussian Exposure Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-35, November.
    13. Abi Jaber, Eduardo & Hainaut, Donatien & Motte, Edouard, 2025. "The Volterra Stein-Stein model with stochastic interest rates," LIDAM Discussion Papers ISBA 2025003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    More about this item

    Statistics

    Access and download statistics

    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:ajf:louvlf:2025001. 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: Séverine De Visscher (email available below). General contact details of provider: https://edirc.repec.org/data/lfuclbe.html .

    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.