Brownian Motion Calculus

Ubbo F. Wiersema

ISBN: 978-0-470-02170-5

Paperback 330 pages

December 2008    

Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. 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.  Summary slides for revision and teaching can be found on the book website.  

Preface.

1 Brownian Motion.

2 Martingales.

3 Itō Stochastic Integral.

4 Itō Calculus.

5 Stochastic Differential Equations.

6 Option Valuation.

7 Change of Probability.

8 Numeraire.

ANNEXES.

A Annex A: Computations with Brownian Motion.

B Annex B: Ordinary Integration.

C Annex C: Brownian Motion Variability.

D Annex D: Norms.

E Annex E: Convergence Concepts.

Answers to Exercises.

References.

Index.