Customer Reviews

Introduction to Stochastic Calculus with Applications

5 star:		(7)
4 star:		(2)
3 star:		(0)
2 star:		(1)
1 star:		(1)

 

 

I had a course of stochastic processes four years ago. A month ago I needed to revive my faded (and very weak) knowledge of stochastic calculus and to learn more as much and as fast as I can. I checked a lot of books about stochastic calculus and financial math, but this book is the best one (of those which I saw) which gives a simple but a rigorous treatment of the subject. If something is not proved then for the case there is an explicit reference to a text. I believe if you have some knowledge of probability it is a very good book to start to learn stochastic calculus.

This is an excellent book on elementary stochastic calculus that is application oriented, and does not get bogged down too much with measure theory. I do not understand the comments of other readers. If they do not have a certain background in real analyis, and some probability theory how can they attempt to learn stochastic calculus. There is no magic book that will teach you stochastic calculus if you don't have some "basic" background in math.To repeat, this book is very good for beginners.

I have to agree with one of the earlier reviewers who rates the book only 3-star. As a reader from engineering background who is determined to grasp the gist of stochastic calculus, I found at the beginning this book hard to carry on. It is only after taking on some readings about theoretical probability and measure theory that I find this book enjoyable. Thus, the statement of 'only a basic knowledge of calculus and probability is required' in the preface is misleading. One has to realize what is considered 'basic knowledge' for mathematicians may not be basic for engineerings, and vice versa.

But, this is indeed an excellent book on the subject without burdening the readers with every rigorous proofs. I would have rated it 5-star if not for the misleading statement. As long as one has a basic knowledge in real analysis, indeed very basic, one will find this book highly enjoyable.

The second edition of this delightful title by Fima C. Klebaner (Monash University, Australia) is a well-written and worthwhile excursion into the realm of stochastic calculus. The text is suited for self-study for a newcomer to the area and there are numerous worked out examples interspersed throughout. Chapters 1 and 2 cover the basics of math and probability/random processes. The author next moves to discuss Brownian Motion and its calculus (the Ito calculus) in chapters 3 and 4. The coverage of the SDEs, diffusions, martingales, semi-martingales, and pure jump processes are included next. Subsequently a chapter on some results concerning the change of probability measure rounds up the theoretical part of the book. There are four final chapters (in the 2nd edition) on applications in finance (stocks, bonds, two fundamental theorems on asset pricing, discussion of various market models), biology (Feller and Wright-Fisher diffusions, branching and birth-death processes, stochastic Lotka-Volterra models) and engineering/physics (filtering and random oscillators) to help satisfy the curiosity of the application-minded readers.

The second edition contains a new chapter on bonds and interest rates, and incorporates more worked-out examples throughout. The discussion of the Stratanovich formulation of Ito's calculus has been moved from the final chapter in the first edition, to the last section of chapter 5 on SDEs. Also at the back of the book there are many answers provided to the selected exercises. For fully grasping the concepts presented, having a background in real analysis and measure theory is helpful but not completely necessary. This was my first book on the subject and it immensely helped me form a fair understanding of the concepts, techniques and terminology of the stochastic calculus. I could only guess that many of you would also benefit from taking up this title at some point in your studies. The only thing that I sensed missing was a glossary with a list of common financial terms for the benefit of those readers who come from a different background. For the science oriented readers, another suggested title is "Stochastic Calculus: Applications in Science and Engineering" by Mircea Grigoriu, which at the same time does a nice job of touching upon the all-important computational methods.

I've seen lot's of other books, (Karatzas, Protter, etc.) but none of them were so well and concisely written. I do recommend this book to anybody who wants to get a quick but still pretty thorough intro to the matter, without spending too much time on the proofs.

This is a very readable text, which is very rare for this subject. Most text on stochastic calculus and Brownian motion rely heavily on measure theory. This text only assumes a familiarity with calculus and concepts in probability theory.

A good introduction to stochastic calculus for students who have a limited knowledge of measure theory (almost everyone except for pure physics and pure maths graduates).

I am fairly new to stochastic calculus, and began my 'travels' with nefti (a very well written text) & bass. I eventually stumbled on this text by klebaner (it was a recommended reading in one of the courses I was researching.) . Eventhough it is more technical than nefti, I found the layout of the book very logical and well ordered.

Klebaner's book is a good next step after an operational grasp of Shreve's Vol-II on continuous time. Klebaner's book (CH 1-10 of 14) enhances the mathematical details (including semi-martingales and jump processes) to the next friendly level. Klebaner gives a number of illuminating {Examples, Remarks}, often, immediately following {Definitions, Theorems}. The chapters 11-14 on applications to finance, biology and engineering are not the strength of the book, and perhaps not intended by the author to be so. Reading the book will reinforce what was learnt in Shreve's, and fill in more details. Possibly a good prelude to the next level book on Stochastic Integration by Protter.

Readers will find that they need advanced calculus to get anything out of this book. Despite what the author states about the book being easy for a beginning derivatives math student to follow, I think you'll find that the level of math needed to keep up with the reading is fairly high level. This is why I gave the book only 2 stars.

The author states that you only need a basic knowledge ofcalculus and probablity. I strongly disagree! Firstly, this book isfull on notation, which makes it feel like you're reading a technical manual rather than a book. The level of mathematical understanding neccesary to get anything out of this book would have included coursework in advanced calculus, ODE, and PDE. I put the book back on the shelf after the first few pages. A much better book for the beginning financial engineer would be Salih Neftci's, which I gave 5 stars to.