This book is designed to serve as a textbook for advanced
undergraduate and beginning graduate students who seek a rigorous
yet accessible introduction to the modern financial theory of
security markets. This is a subject that is taught in both business
schools and mathematical science departments. The full theory of
security markets requires knowledge of continuous time stochastic
process models, measure theory, mathematical economics, and similar
prerequisites which are generally not learned before the advanced
graduate level. Hence a proper study of the full theory of security
markets requires several years of graduate study. However, by
restricting attention to discrete time models of security prices it
is possible to acquire mathematics. In particular, while living in
a discrete time world it is possible to learn virtually all of the
important financial concepts. The purpose of this book is to
provide such an introductory study.
There is still a lot of mathematics in this book. The reader
should be comfortable with calculus, linear algebra, and
probability theory that is based on calculus, (but not necessarily
measure theory). Random variables and expected values will be
playing important roles. The book will develop important notions
concerning discrete time stochastic processes; prior knowledge here
will be useful but is not required. Presumably the reader will be
interested in finance and thus will come with some rudimentary
knowledge of stocks, bonds, options, and financial decision making.
The last topic involves utility theory, of course; hopefully the
reader will be familiar with this and related topics of
introductory microeconomic theory. Some exposure to
linearprogramming would be advantageous, but not necessary.
The aim of this book is to provide a rigorous treatment of the
financial theory while maintaining a casual style. Readers seeking
institutional knowledge about securities, derivatives, and
portfolio management should look elsewhere, but those seeking a
careful introduction to financial engineering will find that this
is a useful and comprehensive introduction to the subject.
General
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