Customer Reviews

Essentials of Stochastic Finance: Facts, Models, Theory

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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.

Before reading this book, I have been quite familiar with stochastic calculus and semi-martingale theory. What interests me most (sometimes puzzles me most) is the way how theory is applied to financial math problems, esp. the justification of certain "conventions" (e.g. we always start with discounted process, play with martingale measures, and do certain standard "rituals" in pricing and hedging). Sometimes people abuse those conventions when the theory's set-up is not quite appropriate. Shiryaev's book shows the justification and limitation of theory, by clearly explaining the origins and specific contexts of theory. This is especially helpful to getting a true understanding of the subject. I would say after reading his book, my mind has achieved a harmony.

I read Shiryaev's book on probability (GTM 95) many years ago. It was a pleasant experience. Now I'm happy to have this kind of experience again. From lines of the book, you can see the author's passion and deep understanding of financial math.
I only regret I didn't read this book much earlier.

The Essentials of Stochastic Finance: Facts, Models, Theory by Albert N. Shiriaev, et al offers a clear treatment of both theoretical and emperical Finance. Shiryaev presents not only the essentials of probability as it is applied to finance,but he also covers recent develpoments in Mathematical Finance. It is very well written and it can be covered in one year (depending on the audience). Each topic moves from the specific to the general, beginning with one or more examples to lead into the theoretical results. This is the most comprehensive book out there. It covers Mathematical Finance, Martingale, Markov Thoery... to Econometric ARCH GARCH FGARCH ...to theory of Finance CAPM APT... PART II of the book requires a good knowledge of Stochastic Calculus at Karatzas and Shreve level...
Outstanding...

This monograph starts from the very basics and develops as it progresses. Its historical notes found all over the book makes it unique and entertaining. As a mathematician aspiring to break through the STREET, I found it very accessible and comprehensive. If you have Brownian Motion and Stochastic Calculus at Shever/Kaaze's (how ever you spell their name) level, you will skim through this book with in weeks. But if you don't, don't panic, you will still be fine with some introductory level measure theoretic probability course.

You will enjoy it as I did.