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Brownian Motion Calculus

Ubbo F. Wiersema
Book information

Publisher: Wiley (West Sussex)
Copyright year: 2010
ISBN: 9780470021705
Medium: Paperback
Pages: 313
Out of print?: N
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Brownian Motion | Martingales | Ito Stochastic Integral | Ito Calculus | Stochastic Differential Equations | Option Valuation | Change of Probability | Numeraire | Annexes | Annex A: Computations with Brownian Motion | Annex B: ordinary integration | Annex C: Brownian Motion Variability | Annex D: Norms | Annex E: Convergence Concepts

Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives, while using several examples of Mathematica. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites.

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Louis Bachelier, Brownian, Gaussian process, Donsker's theorem, Albert Einstein, Girsanov theorem, Feynman-Kac representation, Ornstein-Uhlenbeck, Radon-Nikodym derivative, Savings accounts