This is an
ambitious book. The goal is to walk readers through the mathematics underlying
financial engineering and then illustrate with standard financial engineering
results. The book does just that—in 523 pages.
It is broken into
three parts. The first covers set theory, vector spaces, elementary calculus,
differential equations and integral transforms. The second part takes up measure
theory, measure-theoretic probability and stochastic calculus. The third part,
which comprises fully half the book, covers financial engineering, focusing on
classic equity and fixed income models.
The mathematical
sections are quite formal, adopting a definition, theorem, corollary format.
Proofs are omitted. The material on financial engineering is more of a
formula-laden narrative, although some propositions are formally stated
with thumbnail proofs.
Overall, the book
is quite cryptic. No one is going to learn math and then financial engineering
from scratch using this book. Words are sometimes used without definition, such
as "definitely growing sequence," "elementary event," "valorisation" or "uniperiodical
spot market." The index is just five pages long, which doesn't help.
Another problem is a complete lack of references. Also a table of
standard symbols would have been nice, since I wasn't sure about a few.
Contents
I. CALCULUS
1. Set Theory
2. Linear Algebra
3. Sequences and Series
4. Differential Calculus
5. Integral Calculus
6. Remarkable Functions
7. Complex Numbers
8. Differential Equations
9. Transforms
II. PROBABILITY
10. Measure Theory
11. Probability Theory
12. Stochastic Calculus
13. Stochastic Differential Equations
III. FINANCE
14. Actuarial Calculus
15. Equity Derivatives Models
16. Term-Structure models
This book would
serve best as a reference. The table of contents is quite detailed, allowing
readers to easily locate relevant discussions.
I think, for
readers generally familiar with the topic, the math sections could be especially
handy. Because they are so minimalist, they really tell you what is important. I
have, for example, read far more lengthy discussions of the Radon-Nikodym
derivative than the one presented here, but none were as clear. [December
7, 2006]
.gif)
