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On the combinatorics of iterated stochastic integrals

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  • Jamshidian, Farshid

Abstract

This paper derives several identities for the iterated integrals of a general semimartingale. They involve powers, brackets, exponential and the stochastic exponential. Their form and derivations are combinatorial. The formulae simplify for continuous or finite-variation semimartingales, especially for counting processes. The results are motivated by chaotic representation of martingales, and a simple such application is given.

Suggested Citation

  • Jamshidian, Farshid, 2008. "On the combinatorics of iterated stochastic integrals," MPRA Paper 7165, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:7165
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    File URL: https://mpra.ub.uni-muenchen.de/7165/1/MPRA_paper_7165.pdf
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    References listed on IDEAS

    as
    1. Farshid Jamshidian, 2005. "Chaotic expansion of powers and martingale representation (v1.2)," Finance 0506008, University Library of Munich, Germany.
    2. Nualart, David & Schoutens, Wim, 2000. "Chaotic and predictable representations for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 109-122, November.
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    More about this item

    Keywords

    Semimartingale; iterated integrals; power jump processes; Ito's formula; stochastic exponential; chaotic representation;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

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