To get the free app, enter your email address or mobile phone number.
Stochastic Calculus and Financial Applications (Stochastic Modelling and Applied Probability) Hardcover – October 12, 2000
Elsevier Sales & Deals
Save up to 50% on textbooks, study guides & resources for your medical specialty.
Customers Who Bought This Item Also Bought
More About the Author
Top Customer Reviews
On that note, Steele's book is a MATH book. By contrast, the wonderful book by Baxter & Rennie emphasizes core ideas with emphasis on the relationship between the three primary tools of the discipline (Martingale Representation, Ito-Doeblin Calculus, and the Feynman-Kac formula) while Shreve's classic emphasizes actual development of key models and techniques. Even Oksendal, which is aimed at a slightly more sophisticated mathematical audience, emphasizes applications at the expense of elegance.
In contrast, Steele's book is a math book aimed at Wharton (read: finance and economics doctoral students, likely in their second year) students with varied interests.Read more ›
Mike Steele has used the material in this text to teach stochastic calculus to business students. The text presupposes knowledge of calculus and advanced probability. However the students are not expected to have had even a first course in stochastic processes. The book introduces the Ito calculus by first teaching about random walks and other discrete time processes. Steele uses a lecturing style and even brings in some humor and philosophy. He also presents results using more than one approach or proof. This can help the student get a deeper appreciation for the probabilitist concepts.
The gambler's ruin problem is one of the first problems that Steele tackles and he uses recursive equations as his way to introduce it.
Brownian Motion, Skorohod embedding and other advanced mathematics is introduced and emphasized. After motivating the stochastic calculus and developing martingales Steele covers arbitrage and stochastic differential equations leading up to the fundamental Black-Scholes theory that is important in financial applications. It is not fair to criticize this book for lack of applicability. It is strickly intended to develop a firm theoretical background for the students that will prepare them for a deep understanding of financial models important in applications.
I am not enough of an expert in this area to know if Professor McCauley's criticism in another amazon review of this book is valid, but I do think he is a little too harsh in criticizing the ideology that Steele presents. The ideology is what makes Steele's lectures stimulating and interesting to the students.
Steele, a Wharton Statistics professor, uses financial applications to motivate stochastic calculus from a particular perspective. I have no doubt that he sees stochastic calculus as a field that exists outside of finance and that he does not intend to teach the reader finance theory. His goal, I believe, is to offer a text that is more readable than the classic text of Karatzas and Shreve ("Brownian Motion and Stochastic Calculus"). In my opinion, he has accomplished this goal.
Protter ("Stochastic Integration and Differential Equations: a new approach") does an excellent job, as he is clear and develops the theory in greater generality (using semi-martingales). However, his text is highly theoretical and offers no finance applications. Duffie ("Dynamic Asset Pricing Theory") and Musiela and Rutkowski (above) do not offer the reader the necessary stochastic calculus background.
Lastly, this is a non-trivial subject. For people who do not sit down by themselves and put in the required hours, the outcome will be disappointing.
If you want to learn quant finance at an elementary level, Baxter and Rennie is much, much better. Moreover, if you're comfortable with measure theory,and you want to learn the math that's necessary for option pricing, you'd be better off buying Oksendal's excellent book, which is at least as rigorous as Steele's book but much more clear.
Most Recent Customer Reviews
I am a student, and I have bought this book for supplementary reading for my continuous time models classes. The book was an excellent choice for me. Read morePublished on November 9, 2012 by William Cornett
I felt extremely disappointed to look into this book the minute I received it. I usually love all springer books specially for their top quality presentation. Read morePublished on March 22, 2009 by L. CUNHA
I just got this book. I've been looking at a lot of introductory books on Mathematical Finance, and this seems like one of the best. Read morePublished on February 25, 2009 by S. L. Starr
I find myself wishing again and again that I had discovered this little book years ago. Steele goes through the basics of the parts of the stochastic calculus relevant for... Read morePublished on May 23, 2008 by Alexander Sokol
The book is at the interface of three areas, math, statistics, and finance. While connections between the first two have a long history, it was the connection to finance that... Read morePublished on March 8, 2003 by Palle E T Jorgensen
Reading Steele's book without attending has classes at Wharton leaves the reader looking for explanations to equations. Read morePublished on January 28, 2003
Good intro to stochastic calculus and sde's, can compare roughly with Baxter and Rennie in readability. However, the book unnecessarily propagates ideology. Read morePublished on August 19, 2002 by Professor Joseph L. McCauley