Chaotic expansion of powers and martingale representation

F. Jamshidian

    Research output: Working paper

    8 Downloads (Pure)

    Abstract

    This paper extends a recent martingale representation result of [N-S] for a L´evy 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.
    Original languageEnglish
    Number of pages22
    Publication statusPublished - 16 Jul 2005

    Keywords

    • powerbrackets
    • stochastic integration
    • Martingale representation
    • IR-59847
    • polynomial
    • Chaos
    • Teugels martingales
    • Hilbert space direct sum decomposition
    • stable subspaces

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