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

Farshid Jamshidian
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Farshid Jamshidian: Univ. of Twente

Finance from EconWPA

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.

Keywords: Martingale Representation; chaotic expansion; power brackets; Teugels martingales; Hilbert space; strong orthogonalization (search for similar items in EconPapers)
JEL-codes: G (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2005-06-14
Note: Type of Document - pdf; pages: 22
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0506008

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