Item description for Stochastic Differential Equations: An Introduction with Applications by Bernt K. Oksendal...
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. The new feature of this 5th edition is an extra chapter on applications to mathematical finance.
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Est. Packaging Dimensions: Length: 9.29" Width: 6.15" Height: 0.85" Weight: 1.17 lbs.
Release Date Nov 4, 2002
ISBN 3540637206 ISBN13 9783540637202
Reviews - What do customers think about Stochastic Differential Equations: An Introduction with Applications?
A bit dense for non-Math Quants...but worth pursuing Apr 12, 2008
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. Nov 28, 2007
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! Jul 5, 2007
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!
Excellent introduction on Stochastic Differential Equations May 8, 2007
A well written book in Mathematics 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.
OK intro to stochastic analysis Mar 14, 2007
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).