Chapter

The Mathematics of the Martingale Approach

Tomas Björk

in Arbitrage Theory in Continuous Time

Second edition

Published in print March 2004 | ISBN: 9780199271269
Published online October 2005 | e-ISBN: 9780191602849 | DOI: http://dx.doi.org/10.1093/0199271267.003.0011

Series: Oxford Finance Series

The Mathematics of the Martingale Approach

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This chapter presents the two main workhorses of the martingale approach to arbitrage theory: the Martingale Representation Theorem and the Girsanov Theorem. The Martingale Representation Theorem shows that in a Wiener world, every martingale can be written as a stochastic integral w.r.t, the underlying Wiener process. The Girsanov Theorem gives complete control of all absolutely continuous measure transformations in a Wiener world. Practice exercises are included.

Keywords: martingale approach; arbitrage theory; Martingale Representation Theorem; Girsanov Theorem; Wiener process

Chapter.  5946 words. 

Subjects: Financial Markets

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