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Asset Pricing and Portfolio Choice Theory$
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Kerry E. Back

Print publication date: 2017

Print ISBN-13: 9780190241148

Published to Oxford Scholarship Online: May 2017

DOI: 10.1093/acprof:oso/9780190241148.001.0001

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Brownian Motion and Stochastic Calculus

Brownian Motion and Stochastic Calculus

Chapter:
(p.289) 12 Brownian Motion and Stochastic Calculus
Source:
Asset Pricing and Portfolio Choice Theory
Author(s):

Kerry E. Back

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780190241148.003.0012

Brownian motion and concepts of the Itôs calculus are explained, including total variation, quadratic variation, Levy’s characterization of Brownian motion, the Itô integral, the difference between martingales and local martingales, the martingale (predictable) representation theorem , Itô’s formula (Itô’s lemma), geometric Brownian motion, covariation (joint variation) processes, the relationship between variance and expected quadratic variation, the relationship between covariance and expected covariation, and rotations of Brownian motions.

Keywords:   Brownian motion, Itô integral, Itô process, martingale, martingale representation, local martingale, Itô’s formula, geometric Brownian motion, covariation

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