On the combinatorics of iterated stochastic integrals

F. Jamshidian

doi:10.1080/17442508.2010.539010

On the combinatorics of iterated stochastic integrals

F. Jamshidian

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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.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Stochastics
Volume	83
Issue number	1
DOIs	https://doi.org/10.1080/17442508.2010.539010
Publication status	Published - 2011

Keywords

Itô's formula
EWI-22233
stochastic exponential
MSC-60H05
Semimartingale
IR-81467
chaotic representation
iterated integrals
METIS-289684
power jump processes
MSC-60C05

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Cite this

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title = "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.",

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AB - 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.

KW - Itô's formula

KW - EWI-22233

KW - stochastic exponential

KW - MSC-60H05

KW - Semimartingale

KW - IR-81467

KW - chaotic representation

KW - iterated integrals

KW - METIS-289684

KW - power jump processes

KW - MSC-60C05

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SP - 1

EP - 15

JO - Stochastics

JF - Stochastics

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On the combinatorics of iterated stochastic integrals

Abstract

Keywords

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