Shiryaev A.N., Kruzhilin N. Essentials of Stochastic Finance: Facts, Models, Theory

World Scientific Pub Co Inc – 1999, 852 pages
ISBN: 9810236050, 9789810236052This text provides information for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty. It introduces the reader to the main concepts, notions and results of stochastic financial mathematics, and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and stastical ideas and the methods of stochastic calculus in the analysis of market risks.
This book is typical of Shiryaev, who is a representative of the Russian school of probability theory. Not only the book explains the technical details clearly, but also it explains the "bigger picture" as to why this particular mathematical set-up makes sense and it is a good approximation of reality. The book reflects the (admirable) Russian style of teaching: explain the origins of theory, which are usually some specific problem; then carefully develop a mathematical theory tailor-made for the given problem; finally, disclose the essence of the problem and produce a beautiful result.