Customer Reviews

Stochastic Differential Equations: An Introduction with Applications (Universitext)

5 star:		(11)
4 star:		(7)
3 star:		(2)
2 star:		(2)
1 star:		(1)

 

 

This my recommendation for people who want to learn stochastic calculus for the first time. The virtue of this book is that it keeps matters simple,well grounded, and intuitive enough to hook the newcomers in the subject. Once you get comfortable enough and want to learn technical detail necessary for scholarly research, there are other excellent expositions such as Karatzas and Shreve(1998) and Protter(1990). Some reviews complained that this book is limited to stochastic integration with respect to Brownian motion, but that is precisely why I recommend this book. By starting with Browning motion readers can form concrete mental image of stochastic integration and get ready to stride to more general setting if necessary.
Another virtue of this book is the plenty (easy) exercise problems. Working through them is perhaps the best way to learn stochastic calculus.

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.

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.

It's actually a very good book if you need to learn the topic quickly, armed with a good background in probability theory you will have no difficulty getting through the first 1/3 of the book and gain a working knowledge of SDEs, Ito calculus etc. IT is at times concise in the sense that it lacks motivation etc., but the exposition is such that this presents no major hurdles, as the proofs are clear and short, there are very few errors, except the ones mentioned by the reviewer below, which I should double-check again because I didn't really use this book for its feynman-kac formula (there are better books out there for that). An excellent feature of the book, for those wanting examples from physics and other applied fields, are the problems at the end of chapters. You should definitely give it a try, many of them present the necessary motivation (solutions are at the end of the book). Despite the criticism below, which I consider minor (i.e. it could easily be fixed in a subsequent edition), it is a standard textbook for SDEs, which many respectable mathematicians recommend. Books should be judged by how many times they are quoted by experts, and this book certainly has been cited many times.

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.

The exposition is correct and concise, but too dense for someone without an extensive mathematical background.

I would much rather recommend Shreve's Stochastic Calculus for Finance II. Though longer, it is much more well-motivated and gives you a more intuitive feel for the concepts as opposed to Oksendal's full-on theoreical treatment.

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.

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.

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.

This is a standard work (it is the one I read when I first started looking at this sort of thing) but having taken it off the shelf recently again, I think it is overrated, for several reasons.

First, it is very notation heavy - TeX has seduced Mr. Oksendahl into all sorts of bad habits - I can very easily imagine that the earlier editions (mine is the 5th), which were written with a typewriter, are much more readable.

Second, the proofs are very formal, developed mostly in terms of classical functional analysis (square integrable real functions, geometry of real Hilbert spaces etc.). From the point of view of rigor this is fine, but from the point of view of intuition, not so much, esp. when combined with the heavyweight notation. In fact note that unless you have a decent background in functional analysis, of the sort you are more likely to pick up in a mathematics degree than a finance degree, then you are going to get precisely nowhere with this book.

I don't want to be too negative, and there is lots of good stuff here - just to warn that Oksendahl is not (as one might think) a royal road to the theory of SDEs (depressingly, it may be that Oksendahl is, nevertheless, the best of the bunch out there - it is certainly, all criticism not-withstanding, more accessible than Karatzas and Shreve).