IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpge/0507009.html
   My bibliography  Save this paper

Chaotic expansion of powers and martingale representation (v1.5)

Author

Listed:
  • Farshid Jamshidian

    (Univ. of Twente, NIBCapital)

Abstract

This paper extends a recent martingale representation result of [N-S] for a Levy process to filtrations generated by a rather large class of semimartingales. As in [N-S], we assume the underlying processes have moments of all orders, but here we allow angle brackets to be stochastic. Following their approach, including a chaotic expansion, and incorporating an idea of strong orthogonalization from [D], we show that the stable subspace generated by Teugels martingales is dense in the space of square-integrable martingales, yielding the representation. While discontinuities are of primary interest here, the special case of a (possibly infinite-dimensional) Brownian filtration is an easy consequence.

Suggested Citation

  • Farshid Jamshidian, 2005. "Chaotic expansion of powers and martingale representation (v1.5)," GE, Growth, Math methods 0507009, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpge:0507009
    Note: Type of Document - pdf; pages: 22. Martingale representation results for filtration generated by a large class of processes, including Levy processes. (Minor improvements to version 1.4)
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0507/0507009.pdf
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ariel Neufeld & Philipp Schmocker, 2022. "Chaotic Hedging with Iterated Integrals and Neural Networks," Papers 2209.10166, arXiv.org, revised Jul 2024.

    More about this item

    Keywords

    Martingale representation; stochastic integration; stable subspaces; power brackets; Teugels martingales; polynomial; chaos; Hilbert space direct sum decomposition; Levy processes; finite moements semimartingales; dense.;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G - Financial Economics

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpge:0507009. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.