Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance) (v. 2)

Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance) (v. 2) | Steven E. Shreve | Steven E Shreve Stochastic Calc and Finance 1 and 2

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Stochastic Calculu...

	Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance) (v. 2) Steven E. Shreve Springer, 2008 - 550 pages average customer review:based on 26 reviews view larger image
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highly recommended

Would give 50 stars if I could!

It's quite extraordinary that despite the matchless clarity of this book, there are people who think it deserves only one star. I feel compelled to explain why I think this book deserves not only 5 but perhaps 50 stars.

The book strikes a rare balance between intuition and mathematical precision (by which I do not mean 100% rigor). It's true that the proofs of some deeper mathematical results are only sketched as plausibility arguments and some proofs are altogether omitted, most notably the Martingale Representation Theorem. But this is precisely what makes this book all the more recommendable. Too long a stream of technical mathematical arguments can be an unnecessary strain and distraction for a reader interested in getting a first introduction to the Stochastic Calculus for Finance. For example, in Oksendal's Stochastic Differential Equations, the Martingale Representation Theorem has been proved only after proving a number of auxiliary mathematical results, spanning three to four pages of rigorous mathematics. This book avoids such mathematical distractions, as these details can easily be covered in a second course on stochastic calculus. Having said that, Shreve's definitions and statements of theorems are mathematically precise. Moreover, he gives intuitive discussions of all the results, whether proved or not. And this is the main strength of the book: it combines intuitive explanations with precise mathematical statements in quite an exemplary manner. Before coming to this book, I had read some measure-theoretic probability and basic theory of stochastic processes. But the first time I was able to really appreciate the true significance of things like "F-measurable set", "Borel-measurable function" and "a stochastic process adapted to a filtration" was on reading this book.

A second very attractive feature of this book is the amount of detail in the exercises which clearly shows that the author intends to teach and not tease. In many cases, he guides you through the several stages of a complicated proof. I don't know about others, but this made me do a lot more exercises on my own than I could have done otherwise and this boosted my self-confidence tremendously. Besides, the exercises are not just dry mathematical proofs and derivations, but many are based on financial applications.

Thirdly, there are hardly any instances of "it's readily seen that..." or "it is easy to verify...", i.e. important steps in derivations of results are not omitted, even though that sometimes means some repetition. But repetition is essential to remembering precise mathematical statements correctly. With reasonable mathematical maturity (let's say advanced calculus at the level of Tom Apostol's Mathematical Analysis), one can derive all the results in the text. I am not sure one can say the same for many other texts on probability or stochastic calculus.

Fourthly, the book covers pretty much the entire spectrum of classical mathematical finance, including a chapter on jump processes. Of course, being a first introduction to the subject, there is little on cutting-edge topics like Levy processes and variance gamma. But making a first introduction all-inclusive would defeat the whole purpose of the text being a first introduction.

CONCLUSION: THE BEST BOOK FOR A FIRST INTRODUCTION.

P.S. For the mathematically insatiable, Professor Shreve has co-authored an as-rigorous-as-it-gets "Brownian Motion and Stochastic Calculus". They have my free invitation!

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Steven E Shreve Stochastic Calc and Finance 1 and 2

These two books are a definite buy for anyone interested in getting a introduction into stochastic calculus and finance. I used these books for my course in Stochastic Calculus at Univ of Chicago. The book is a very good introduction to stochastic calc and application to finance.

The first book deals with discrete time models and the second moves on the continuous time setting. The books are self contained and the material is presented in a manner that can be understood by most people with basic calc and probability theory.

good

very good

reviews: 1, 2, 3, page 4, 5, 6

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