Stochastic Calculus for Finance II: Continuous-Time Models

by Steven E. Shreve

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Genres: Finance, Mathematics, Textbooks, Economics, Business, Science, Reference

569 pages, Paperback

First published April 25, 2004

Reviews

[Gabriel Tan]

I believe the greatest challenge for readers—especially those without a solid mathematical background—is the book’s dense mathematical content. Nevertheless, I thoroughly enjoyed the level of rigor in Shreve’s second volume, which, like the first, was highly recommended by my professor, who described stochastic calculus as the “bread and butter” of any quantitative finance professional.

Each chapter builds upon the previous one, covering what you’d expect from a comprehensive text on stochastic calculus, including martingale theory, the Black–Scholes framework, and Girsanov’s theorem. Similar to works by authors like Paolo Baldi, Shreve’s approach provides an in-depth exploration of these core topics.

I will certainly revisit this book, as I believe there is still more knowledge to extract from its pages.

[Jonathan Lin]

Read up to, but not including, chapter 5 for fun. I found the textbook extremely dense and sometimes hard to understand (needed ChatGPT to explain some of the proofs). But this was an interesting read overall, and it stimulated my brain.

May finish the rest of the book if I ever try out the QR career track.

[Daniel]

Accessible and practical overview of modern stochastic finance: a deeper dive.

[Toivo Haapasaari]

It’s alright, the book does what its supposed to but kind of fails to juggle both rigor and applications. I guess the books alright for the finance stuff and might be good for intuition.

Didn’t do the later chapters instead left for Protters stochastics book. Also studied some of Shreve’s other work with Karatzas namely Brownian mortion and Stochastic calculus which was in terms of rigor, very different.

The book might be a bit overhyped but it does what it promisses, I guess.

[Andrew Jackson]

Thrilling from beginning to end.

I did sometimes think the presentation of stochastic analysis was slightly perfunctory as the book is a little light on the "stochastic calculus" and perhaps a little heavy on the "for finance."

[Jing Ren]

I have read and derived the book countless times. But there is not much to be said about it because it is beautifully written. In a few cases, I have to resort to other books or lecture notes for a thorough understanding though. Shreve speaks in the language of mathematics, so sometimes I need to dig harder for the intuitions. But I like his writing style.

I wouldn't judge the book by its comprehensiveness because it is just a starter for this field. However, I do need to share some critique. The quality of the exercise questions is very high in the first few chapters, and declines as the book progresses. I have even found a question in chapter 10 with conclusions that are wrong in a major way.

[Jing Ren]

If not for the reason that there is no alternative, I really dislike the book. The author never says what he is doing before I have to go through a very long paragraph and figure it out myself. And he also seems to forget what he has written before. I particularly dislike the part solving stochastic PDE's when he is always like "This is the solution and now let's prove it is correct." even in the exercises. But there is no gain of conciseness. To me it seems he intentionally keeps things vague to avoid being criticized for lack of rigor.

[Joe Malicki]

If I'm going to learn stochastic calculus this rigorously, I want more in-depth treatment of Ito's lemma and the like to know how much to believe it and what the proofs really depend on.

If you're not going to go full out, then why not just grab a quick primer on Ito's lemma without all the background?

(admittedly this book is probably better in that respect than just about any other finance-focused text I've seen, but still, what's the utility in the middle ground?)

[Austin]

This is the best, most readable book on this topic (though make no mistake, it is still a graduate level mathematics text). The .pdf of Shreve's lecture notes that eventually became this book have had a loyal following on the net for years. This should be on every quant's shelf.

[Adam]

The single book I have spent most time on. Steve Shreve is my professor of this course. He gives wonderful lectures. His understanding in math and finance helps a lot to understand the formulas of this book. His passion in teaching and skills in communication is truely inspiring.

[Peng Gao]

Lacks depth once the author finishes borel algebras ;)) stochastic PDE is not developed in any way. Just remember Feynman-Kac and you are good to go lol