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Methods of Mathematical Finance (Stochastic Modelling and Applied Probability) Corrected Edition

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Ioannis Karatzas (Author)
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Ioannis Karatzas (Author), Steven Shreve (Author)
4.2 out of 5 stars 5 customer reviews
ISBN-13: 978-0387948393
ISBN-10: 0387948392
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Product Details

  • Series: Stochastic Modelling and Applied Probability (Book 39)
  • Hardcover: 416 pages
  • Publisher: Springer; Corrected edition (September 21, 2001)
  • Language: English
  • ISBN-10: 0387948392
  • ISBN-13: 978-0387948393
  • Product Dimensions: 6.1 x 0.9 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #1,227,571 in Books (See Top 100 in Books)

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Top Customer Reviews

5.0 out of 5 starsOne of the best
By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on June 30, 2001
Format: Hardcover
The application of highly sophisticated mathematical techniques to finance is now commonplace and is considered also of great practical importance. Mathematical modeling in finance is now very entrenched in investment houses and trading firms and this will only increase in years to come. This book is an excellent overview of mathematical finance and is written for mathematicians who have no background in finance. The book could be read easily by anyone with background in stochastic processes at the level of the author's earlier book "Brownian Motion and Stochastic Calculus". Since it is written for mathematicians, it follows a "definition-theorem-proof" format. However the authors do interject a lot of explanation into the dialog, especially that concerning finance.

Chapter 1 is an overview of a Brownian motion model of financial markets. Financial assets are considered to have prices evolving continuously in time and driven by Brownian motion. They do however g!ive references for models that assume discontinuous asset prices. The authors define a financial market rigorously in terms of (progressively) measurable processes for the risk-free rate, mean rate of return, dividend rate, and volatility. The after a discussion of portfolio, gains, income, and wealth processes, the authors define a notion of a viable market, namely one where there are no arbitrage opportunities. They then define standard and complete financial model and characterize their properties in terms of martingales.

Chapter 2 is a treatment of options pricing theory, with the assumption of a complete standard, financial market. These contingent claims are given a brief historical introduction at the beginning of the chapter.Read more ›
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5.0 out of 5 starsThe acme of rigorous mathfin, not for the faint hearted
By Bachelier on September 7, 2005
Format: Hardcover Verified Purchase
For those working in higher levels of pure mathematics or physics Ioannis Karatzas's and Steven E. Shreve's Methods of Mathematical Finance will be the most accessible for helping you understand what all the fuss is about in finance and Wall Street. From the groves of academe, finance as it is practiced looks like so much "nonsense on stilts." However, serious intellectual work has been done examining finance and transactions under limits, spaces, stochastic paths and operators, and this work is the most rigorous explication of the foundations of this thinking, and its most natural extensions and applications.

This work is explicitly not for MBAs or other `phynance-lite" types who view interest rates as single factor driven and think the alpha and omega of option pricing as the Black-Scholes model. While the work rigorously addresses interest rates and option pricing from a mathematical standpoint, it is better thought of as applying Brownian motion to contingent events and time series, which for the purposes of this volume are financial values and the volatility of outcomes.

Another audience will be advanced students studying financial engineering or mathematical finance. This book is foundational required reading in most of the French DEA programs dealing with stochastic applications to finance.
One major caution: unless you have an intuitive grasp of programming from reading math presented in the "definition-theorem-proof" form of academia, you will be at a loss as to how to bridge this work to a practical application. I know of students who floundered around with Mathematica and this volume before coming across more accessible works written for practitioners and programmers in mind. This work is for those well trained in mathematics who want to learn about finance. For learning about programming optimal savings and consumption portfolios, option prices, etc. other works, such as those by Mark Joshi, are your better choice.
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4.0 out of 5 starsOnly for the most mathematically inclined
By C. Ang VINE VOICE on July 17, 2009
Format: Hardcover Verified Purchase
This is the most mathematically rigorous treatment of asset pricing that is available. That's why this gets 4 stars. But this book is certainly not for everyone, which is why the 1 star is left out.

I am not kidding when I say this book is only for the most mathematically inclined. I have read many texts that require a decent amount of mathematics and I have already encountered the concepts that are discussed in this book, and I still found it quite a challenging read. In my opinion, you need to have a good grasp of probability and random processes to enjoy this book. For those who would like a lighter read, I suggest looking into Cochrane's Asset Pricing, LeRoy and Werner's Principles of Financial Economics, or even Skiadas' Asset Pricing Theory.

As a general matter, this book covers the major topics in asset pricing (e.g., financial markets, contingent claims, complete markets, consumption, investment, hedging, etc.) If you are technically inclined and you are up for the challenge, you should go ahead and read this book by all means. It is a very good book with little or no fluff.
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2.0 out of 5 starsNOT a stand-alone book
By J. Holman on April 23, 2004
Format: Hardcover
Very rigorous and methematically precise, but how can this text not even mention Ito's lemma? Well, because it isn't really a "sequel to Brownian Motion and Stochastic Calculus by the same authors" but more like the second half of that book. Unless you have their BM&SC or another similar reference by your side you won't get very far . . . and this fact is not at all apparent from reading the editorial description or jacket review.
For a self-containted text with both the basic math background AND the finance I recommend either Lamberton and Lapeyre (fairly complete but with some technical proofs referred to BM&SC) or Joshi (lots of applications, less mathy). Neither of these will be as comprehensive or rigorous as the 2-volume Karatzas and Shreve but both are good introductions to the subject.
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