PDF Ebook Brownian Motion Calculus, by Ubbo F. Wiersema
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Brownian Motion Calculus, by Ubbo F. Wiersema
PDF Ebook Brownian Motion Calculus, by Ubbo F. Wiersema
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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.
- Sales Rank: #827157 in Books
- Published on: 2008-12-08
- Original language: English
- Number of items: 1
- Dimensions: 8.94" h x .80" w x 6.00" l, 1.10 pounds
- Binding: Paperback
- 330 pages
From the Back Cover
Brownian Motion Calculus
Ubbo Wiersema
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. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete-time setting. The continuous-time equivalent requires a new concept, the Itō stochastic integral. Its construction is explained step by step, using the so-called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is Itō’s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so-called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so-called numeraire. 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 www.wiley.com/go/brownianmotioncalculus.
About the Author
UBBO WIERSEMA was educated in Applied Mathematics at Delft, in Operations Research at Berkeley, and in Financial Economics and Financial Mathematics at the London School of Economics. He joined The Business School for Financial Markets (the ICMA Centre) at the University of Reading, UK, in 1997, to develop and teach its curriculum in Quantitative Finance. Prior to that, he was a derivatives mathematician at the merchant bank Robert Fleming in the City of London. Before that his career was focused in Operations Research in the US and Europe.
Most helpful customer reviews
21 of 21 people found the following review helpful.
much needed missing link
By Louis Charbonneau
This is an awesome book!
It follows a non-rigorous (non measure-theoretic) approach to brownian motion/SDEs, similar in that respect to the traditional calculus textbook approach. The author provides plenty of intuition behind results, plenty of drills and generally solves problems without jumping any intermediate step.
I have read most books of the kind and this one is clearly the best. It is suitable for undergraduate education, namely in engineering and in finance. It may be a bit on the light side for maths undergrads, although could be used for a light intro to these topics.
12 of 12 people found the following review helpful.
Excellent Introduction Without the Abstract Math Approach
By C T
This is really the best introduction book on the subject matter I have ever read. If you are not a current student in shool or newly graduate with math training, or a math teacher, but have some general college math training then this book is the best introduction for you on this subject. Although I had read some basic abstract math starting with the set theory long time ago, it took me too much time to proceed in reading standard intro math to financial engineering. Thanks to the author's introduction, when I come back to those FE math it feels SO easy now.
7 of 7 people found the following review helpful.
excellent introduction
By quant
i have some familiarity regarding brownian motion. Many stochastic calculus books go into deep mathematical reasoning. I really enjoyed the authors approach to the problem. This is clearly the way one should start into the subject prior to starting an MFE program. Then after reading the book, one can read the book by sean dineen etc or other stochastic calculus books which go into more rigorous detail. This book must not be missed by any chance. It will give you an edge in MFE programs knowing this material. He has written this book in the same style as many calculus books which is very helpful. Once you master this book, you can go into a move proof based subject matter.
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