This book presents a concise treatment of stochastic calculus and its
applications. It gives a simple but rigorous treatment of the subject
including a range of advanced topics, it is useful for practitioners who
use advanced theoretical results. It covers advanced applications, such
as models in mathematical finance, biology and
engineering.Self-contained and unified in presentation, the book
contains many solved examples and exercises. It may be used as a
textbook by advanced undergraduates and graduate students in stochastic
calculus and financial mathematics. It is also suitable for
practitioners who wish to gain an understanding or working knowledge of
the subject. For mathematicians, this book could be a first text on
stochastic calculus; it is good companion to more advanced texts by a
way of examples and exercises. For people from other fields, it provides
a way to gain a working knowledge of stochastic calculus. It shows all
readers the applications of stochastic calculus methods and takes
readers to the technical level required in research and sophisticated
modelling.This second edition contains a new chapter on bonds, interest
rates and their options. New materials include more worked out examples
in all chapters, best estimators, more results on change of time, change
of measure, random measures, new results on exotic options, FX options,
stochastic and implied volatility, models of the age-dependent branching
process and the stochastic Lotka-Volterra model in biology, non-linear
filtering in engineering and five new figures.Instructors can obtain
slides of the text from the author.
