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Title: Stochastic Differential Equations: An Introduction With Applications (Universitext) by B. K. Ksendal, Bernt Oksendal ISBN: 3-540-04758-1 Publisher: Springer Verlag Pub. Date: December, 2003 Format: Paperback Volumes: 1 List Price(USD): $44.95

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Average Customer Rating: 4.5 (6 reviews)

Rating: 5
Summary: An Excellent Book
Comment: When I became a quant, I needed to learn stochastic calculus and stochastic differential equations. Luckily, I found this book, which covers a lot of difficult concepts in a rigorous but accessible way. Oksendal is an excellent writer: his proofs are very clear (and usually not too terse), he provides very illustrative examples, and he does a great job of anticipating where the reader might get stuck. In addition, the problems at the end of the chapters do a good job of reinforcing central theorems and ideas. After reading this book, you'll be able to read most of the academic financial literature and all finance textbooks.

I've read lots of math books, and this is undoubtedly the best one I've ever seen. The only necessary backround is a solid understanding of measure theory.

Rating: 4
Summary: Good reference - not so good text-book
Comment: This book is excellent if you already know why you want to know the material in it. Then it is concise, to the point, and very well-written. I turn back to it over and over again; my copy is very worn by now.

When I first started reading it, I was not too pleased with it. As a text-book it suffers from not motivating the theory, and not connecting it with parallel approaches. The subtitle mentions applications. Now, what one person considers applications is what the next person considers abstractions. My point of view is truly applied - I want to use SDE's to model real-world phenomena (actually, not financial ones) and are less interested in SDE's per se. So I would have liked more connections with physics (for instance advection-diffusion transport phenomena) and I would have liked the material to be more solidly anchored in general stochastic processes. Nevertheless, I appreciate that the book wouldn't have been as concise, then.

Rating: 5
Summary: Simple, but rigorous book
Comment: This a perfectly written book on stochastic calculus, especially needed for junior (but rising!) financial quants. All themes are carried out with a profound pedagogical talent. For a practitioner, the book loses nothing to Karatsas and Shreve, but is a much shorter, simpler and joyable reading. Yet, it is a systematic text book that covers most classical results with (important!) accessible proofs. For example, the Kolmogorov equations (forward and backward) are derived, not just stated as in most other texts, Girsanov's theorem is relatively well covered (although the author has not demonstrated its computational side well enough, but this is a common disease). Ideas are illustrated by practical problems (including those from quantitative finance). What I also liked, Oksendal's SDE theory is much closer to "differential equations", than what is often presented by probabilists. A must for every practitioner who works with stochatic processes.

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