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Chaotic expansion of powers and martingale representation (v1.2)

Author

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  • Farshid Jamshidian

    (Univ. of Twente)

Abstract

This paper extends a recent martingale representation result of [N-S] for a L\'{e}vy 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 (v1.2)," Finance 0506008, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0506008
    Note: Type of Document - pdf; pages: 22
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0506/0506008.pdf
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    Cited by:

    1. Jamshidian, Farshid, 2008. "On the combinatorics of iterated stochastic integrals," MPRA Paper 7165, University Library of Munich, Germany.
    2. 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; chaotic expansion; power brackets; Teugels martingales; Hilbert space; strong orthogonalization;
    All these keywords.

    JEL classification:

    • G - Financial Economics

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