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Rating: 
Summary: Practical review of Oksedal's SDE's (wrt finance)
Review: As a so-called practicising 'quant' in a top Wall Street Investment bank, I came upon this book from colleagues who raved about the exposition of the material found in this book.Indeed even though I have an engineering and advanced mathematical background, I find the material to be useful in helping to understand the more research oriented finance journals. From a practitioner's view point the most fundamental aspect of the book is the statement where it states the solutions of SDE's can be thought of as inherent Browian motions for it is the latter which enables one to price the financial instruments one commonly hears of in the press.I would recomend first understanding the physical and mathematical aspects of Browninan motion before tackling the abstract field of stochastic calculus so that meaningful interpretations can be drawn.Nevertheless the book gives excellent penetrating coverage of what SDE's are.For budding so-called 'rocket-scientists' who want to make mega-bucks on the markets, my advice would be to first master partial differential equations (because this is the only way to pragmatically price things like exotic derivatives) then for their own enlightenment they can read this book if only just to keep up with the jones's.
Rating: 
Summary: Wrong Kolmogorov backward equation
Review: His version of Kolmogorov backward equation(Theorem 8.1.1, p. 131) is just wrong. Of course, then his Feynman-Kac formula(Theorem 8.2.1, p. 135) is wrong as well.
The correct versions can be found in numerous other books, like
Karatzas and Shreve, Shreve II(2004), Gikhman and Skorokhod, and on and on.
Rating: 
Summary: Laudable Goal, Poor Execution
Review: If calculus is to real analysis then this book is an attempt at filling in _____ is to stochastic analysis. Stochastic analysis is a difficult topic and a simplified introduction with minimal prerequisites is a great goal. However, this book has not fullfilled its promise.
There are a number of complaints to be made about this book. Most importantly is that in his attempt at simplification, Oksendal frequently chooses shedding (important) details over properly motivating a new concept. I found this particularly true in his exposition of generators. The book is poorly also organized: a number of topics are arbitrarily split into different chapters, important ideas hide inside of examples, etc.
While this is not my favorite book by any means, there is currently no replacement for it. Jumping directly into a book like Karatzas&Shreeve can be daunting. I would recommend getting a used copy. Also, previous editions seem to be very nearly identical to the current edition.
I also recommend checking out Rogers&Williams "Diffusions, Markov Process, and Martingales" Vols I&II.
Rating: 
Summary: An Excellent Book
Review: 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.
Rating:
Summary: Simple, but rigorous book
Review: 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.
Rating:
Summary: Good reference - not so good text-book
Review: 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:
Summary: An excellent introductory book to SDEs
Review: This book is very easy to follow through the basics of stochastic calculus. The writing and examples remain fluid throughout the book, but the more difficult material could use a bit more in the way of examples.
Rating:
Summary: Good entry level primer
Review: This book is very easy to follow through the basics of stochastic calculus. The writing and examples remain fluid throughout the book, but the more difficult material could use a bit more in the way of examples.
Rating:
Summary: An excellent introductory book to SDEs
Review: This is a book I recommend as a TA in a mathematical finance Masters program. It gives a mathematically rigorous presentation of Stocastic Differential Equations without getting bogged down in too much detail, as do many books from a probability/stochastic processes background. It also illustrates the beautiful connection between SDEs and the heat equation. I recommend this book to anyone trying to read Karakas and Shreve for the first time.
Rating:
Summary: An Excellent Book
Review: 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.
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