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

Farshid Jamshidian
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Farshid Jamshidian: Univ. of Twente, NIBCapital

GE, Growth, Math methods from EconWPA

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.

Keywords: Martingale representation; stochastic integration; stable subspaces; power brackets; Teugels martingales; polynomial; chaos; Hilbert space direct sum decomposition; Levy processes; finite moements semimartingales; dense. (search for similar items in EconPapers)
JEL-codes: C G (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fin
Date: Written 2005-07-15
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)
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