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Title: NOT a stand-alone book
Review: 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.
