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Introduction To Stochastic Calculus With Applications (3Rd Edition) Paperback – 21 Mar 2012

3.6 out of 5 stars 7 customer reviews

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Product details

  • Paperback: 452 pages
  • Publisher: Icp; 3rd Revised edition edition (21 Mar. 2012)
  • Language: English
  • ISBN-10: 1848168322
  • ISBN-13: 978-1848168329
  • Product Dimensions: 15.2 x 2.6 x 22.9 cm
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Bestsellers Rank: 1,022,676 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

Review

It contains many worked out examples while the stochastic calculus is presented in a concentrated but transparent form. -- Professor Robert Liptser, Tel Aviv University --This text refers to the Hardcover edition.

From the Inside Flap

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.

This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.

In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises.


Customer Reviews

3.6 out of 5 stars
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Top Customer Reviews

Format: Hardcover
There are numerous books on the subject of stochastic calculus, specially with emphasis on the financial applications. This delightful title by Fima C. Klebaner (Monash University, Australia), now in its 2nd edition, is a well-written and worthwhile excursion into the realm of this important area of mathematical sciences. The text is suited for self-study for a newcomer and there are quite a few 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.
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Format: Paperback
This is quite a technical book on Brownian motion and stochastic calculus. The ordering of the chapters is really good, as it's progressive and introduces concepts progressively, from Brownian motion to semi-martigales and diffusion process. However this is not a book for the faint-hearted, as the mathematical description are thorough and most are demonstrated thoroughly. What makes this book self-contained is the list of exercices at the end of each chapter; half of which being corrected or including tips. Applications given for mathematical finance might not be the clearest available on the market (but could be an ideal companion for the Baxter & Rennie), but it gives a solid background to understand diffusion models.
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Format: Kindle Edition
This book is really well put together.

The content itself is great and it only needs a modicum of maths and calculus knowledge. (Not sure about readability on Kindle, as per other reviewer negative feedback.)

Highly recommend to finance quants both junior and senior.
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Format: Paperback
I am reading for a PhD degree in finance in a business school in UK. I did an undergrad in Engineering. Although this book may be difficult for non-mathematicians like myself, I find this book extremely useful!! As a PhD student who is working on asset pricing -- in particular, derivatives, I do not care much, at this stage, of rigorous proofs of mathematical results. Sketches of proofs on some advanced results are perfectly fine, so long as they make sense to me. This book provides rigorous yet accessible treatments of the subject. This has allowed me to gain the knowledge on stochastic calculus quicker. Examples and exercises are very helpful. Personally, I think this book is suitable for PhDs or above, unless you are a mathematician.
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