IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v193y2023ics0167715222002164.html
   My bibliography  Save this article

A transitivity property of Ocone martingales

Author

Listed:
  • Zhang, Jichen
  • Chen, Zengjing

Abstract

This paper gives a sufficient condition to make an Ocone martingale still an Ocone martingale after an integral transformation. Let θ be an Ocone martingale, Mt=∫0tαsdθs. Then M is an Ocone martingale if α and θ are conditionally independent given 〈θ〉. The converse problem is still open, but a partial converse theorem is obtained for a special class of Ocone martingales, which greatly generalizes Theorem 3 proposed by Vostrikova and Yor (2000). The results of this paper can be used to determine whether a local martingale is an Ocone martingale, as well as to construct more complex examples of Ocone martingales.

Suggested Citation

  • Zhang, Jichen & Chen, Zengjing, 2023. "A transitivity property of Ocone martingales," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002164
    DOI: 10.1016/j.spl.2022.109703
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222002164
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109703?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. Chaumont, L. & Vostrikova, L., 2009. "Reflection principle and Ocone martingales," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3816-3833, October.
    2. Tang, Qihe & Tong, Zhiwei & Yang, Yang, 2021. "Large portfolio losses in a turbulent market," European Journal of Operational Research, Elsevier, vol. 292(2), pages 755-769.
    3. Rheinländer, Thorsten & Schmutz, Michael, 2013. "Self-dual continuous processes," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1765-1779.
    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. Tang, Qihe & Tong, Zhiwei & Xun, Li, 2022. "Portfolio risk analysis of excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 91-110.
    2. Luca De Gennaro Aquino & Carole Bernard, 2019. "Semi-analytical prices for lookback and barrier options under the Heston model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 715-741, 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:stapro:v:193:y:2023:i:c:s0167715222002164. 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.