Product Description

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.

Product Details

• Amazon Sales Rank: #55128 in Books
• Published on: 2007-06-12
• Number of items: 1
• Binding: Paperback
• 374 pages

Review

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)

Book Info
Text states six problems in the introduction in which stochastic differential equations play an essential role in the solution. The author returns to these problems while developing stochastic calculus to show how the theory works. Includes new exercises and worked solutions. For graduate students. Previous edition: c1998. Softcover. DLC: Stochastic differential equations.

Customer Reviews

A bit dense for non-Math Quants...but worth pursuing
If you aren't a bit of a Math wonk, this book can be a bit daunting. But it is worth wading through the Math if you want to understand the "WHY" behind all those formulas and results. If you are looking for a gentler introduction and the "real formulas" Quants use, check out Paul Wilmott's books.

The text generally starts with an intuitive example for the chapter and then starts methodically working through the underlying mathematics to get to the meaty results. The exercises are worth the effort as they reinforce the chapter work and offer additional insights.

The best book for a first grad course on Stochastic Calculus.
Oksendal is not as formal as KS, Karatzas and Shreve (Brownian Motion and Stochastic Calculus), but it is easier to follow. The exercises in the first five chapters are very informative. Exercises in last chapters are more difficult (as they should be). After studying by this book, you may want to go deeper by using KS.

A very good book!
I read this book after I had read Karatzas' and Shreve's book "Stochastic Calculus..." and it is probably better to do it the other way round. The mathematical prerequisites are not high, however a good intuitive understanding of measure theory is probably necessary. The pace of the book is leasurely, the proofs are such, that pencil and paper is rarely needed, however no rigor is lost.
The book quickly moves to interesting applications of the theory, which is motivated very well.
It contains a few typographical errors, mostly in the last chapter, and mostly of a harmless nature.

With the necessary mathematical background, it seems to be an ideal introduction to this highly interesting topic of stochastic differential equations!