Introduction to Stochastic Calculus with Applications |  | Author: Fima C. Klebaner
Publisher: Imperial College Press
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Rating:  10 reviews
Sales Rank: 219361
Media: Paperback
Edition: 2
Pages: 432
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Dimensions (in): 8.8 x 6 x 0.9
ISBN: 186094566X
Dewey Decimal Number: 519.2
EAN: 9781860945663
ASIN: 186094566X
Publication Date: June 30, 2005
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Product Description
This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering. Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling. This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka Volterra model in biology, non-linear filtering in engineering and five new figures. Contents: Preliminaries from Calculus; Concepts of Probability Theory; Basic Stochastic Processes; Brownian Motion Calculus; Stochastic Differential Equations; Diffusion Processes; Martingales; Calculus for Semimartingales; Pure Jump Processes; Change of Probability Measure; Applications in Finance: Stock and FX Options; Applications in Finance: Bonds, Rates and Options; Applications in Biology; Applications in Engineering and Physics.
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Showing reviews 1-5 of 10
 Stochastic Calculus October 31, 2008
ssfsumit (Massachusetts)
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.
Splendid text, but perhaps a bit lost in the shuffle. May 14, 2006
Farshid Arjomandi (California, USA)
8 out of 8 found this review helpful
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.
A good book with yet misleading intro March 14, 2003
9 out of 9 found this review helpful
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.
Excellent introduction to stochastic processes December 1, 2002
0 out of 3 found this review helpful
This is a very nice book. Looking forward to the 2nd edition with more material particularly on interest rate models.
One of the best concise and readable books on the subject October 1, 2002
3 out of 3 found this review helpful
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.
Showing reviews 1-5 of 10
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