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

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  • Farshid Jamshidian

    (Univ. of Twente)

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    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.

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    File URL: http://128.118.178.162/eps/fin/papers/0506/0506008.pdf
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    Bibliographic Info

    Paper provided by EconWPA in its series Finance with number 0506008.

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    Length: 22 pages
    Date of creation: 14 Jun 2005
    Date of revision:
    Handle: RePEc:wpa:wuwpfi:0506008

    Note: Type of Document - pdf; pages: 22
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    Web page: http://128.118.178.162

    Related research

    Keywords: Martingale Representation; chaotic expansion; power brackets; Teugels martingales; Hilbert space; strong orthogonalization;

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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.

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