On the combinatorics of iterated stochastic integrals

Jamshidian, Farshid (2008): On the combinatorics of iterated stochastic integrals.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Semimartingale; iterated integrals; power jump processes; Ito's formula; stochastic exponential; chaotic representation
• Subjects: C - Mathematical and Quantitative Methods > C0 - General

References

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