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Stochastic Differential Equations: An Introduction with Applications (Universitext) Paperback – September 22, 2010
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From the reviews of the fifth edition:
"This is a highly readable and refreshingly rigorous introduction to stochastic calculus. … This is not a watered-down treatment. It is a serious introduction that starts with fundamental measure-theoretic concepts and ends, coincidentally, with the Black-Scholes formula as one of several examples of applications. This is the best single resource for learning the stochastic calculus … ." (riskbook.com, 2002)
From the reviews of the sixth edition:
"The book … has evolved from a 200-page typewritten booklet to a modern classic. Part of its charm and success is the fact that the author does not bother too much with the (for the novice) cumbersome rigorous theory … . This does not mean that the book is not rigorous, it is just the timing and dosage of mathematical rigour … that is palatable for undergraduates … . a highly readable account, suitable for self-study and for use in the classroom." (René L. Schilling, The Mathematical Gazette, March, 2005)
"This is the sixth edition of the classical and excellent book on stochastic differential equations. The main difference with the next to last edition is the addition of detailed solutions of selected exercises … . This is certainly an excellent idea in view to test its ability of applications of the concepts … . certainly one of the best books on the subject, it will be very helpful to any graduate students and also very valuable for any analysts of financial market." (Stéphane Métens, Physicalia, Vol. 26 (1), 2004)
"This is now the sixth edition of the excellent book on stochastic differential equations and related topics. … the presentation is successfully balanced between being easily accessible for a broad audience and being mathematically rigorous. The book is a first choice for courses at graduate level in applied stochastic differential equations. The inclusion of detailed solutions to many of the exercises in this edition also makes it very useful for self-study." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1025, 2003)
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Top Customer Reviews
Another virtue of this book is the plenty (easy) exercise problems. Working through them is perhaps the best way to learn stochastic calculus.
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.
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.
Stochastic Differential Equations is a branch of mathematics. This book is not just for financial derivatives analysis or modeling. Oksendal first introduces the subject by raising a few stochastic problems (population growth; electric charge in RLC circuit; filtering problems, Dirichlet problems; asset management; optimal portfolio and options pricing) in the first chapter. The subsequent chapters develop notions and techniques which are able to solve wide varieties of stochastic problems (not just those mentioned in the first chapters). The arrangement is impressive in particular for readers who have no previous knowledge about the subject. The readers at least know the target for developing the techniques and would not lose the way when manipulating tons of symbols. Hints and answers to selected problems are invaluable to students for self-study.
To achieve a sound background on stochastic equations is extremely important especially in quantitative finance. It is not an easy job however. QF students may consider going through this book before seriously take Shreve's books on Stochastic Calculus for Finance.
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).
Most Recent Customer Reviews
A classic. Written with an advanced reader in mind, this book covers most topics of stochastic calculus in great detail and with sufficient clarity. Read morePublished 1 month ago by Daniel C
if you are a math people, please avoid this book because it will make you feel very uncomfortable!! the proofs are full of bugs and the logic is very unclear --- so I even cannot... Read morePublished on February 26, 2014 by Zhanxiong Xu
Oksendal's book is well written and covers a lot of material.
No surprise it's a standard reference in SDE classes.
This is a great book for anyone wanting to learn about stochastic calculus, particularly if you are interested in working in finance or if you want to a broad overview of the... Read morePublished on March 2, 2013 by Ole Jastrau
The book makes us understand the actual importance of the probability.
Today the books about the stochastic equations have superated the interest of the traditional... Read more
The title says it all. It is an excellent book for beginners to get in to stochastic calculus. A small suggestion that you revise your ODE before you tackle this book as it will... Read morePublished on September 2, 2012 by LK
This book is offers an excellent introduction to SDE but limiting the text to integration w.r.t Brownian motion. Read morePublished on January 14, 2012 by Amazon Customer
It is a well written, concise text, suitable both for beginners (the appendices are excellent) and experienced readers. Various topics are covered in sufficient detail. Read morePublished on March 20, 2011 by An avid reader from Europe