This book is an excellent text on stochastic calculus. As is commonly done, the text focuses on integration with respect to a Brownian motion.
However, there are several important pre-requisites: the reader must be intimately familiar with measure theory, probability theory and stochastic processes. For those new to stochastic calculus it is generally recommended to read Oksendal's book on stochastic differential equations and then come back to Karatzas and Shreve.
Please be warned that even with reasonable background to probability theory and stochastic calculus, this text is very difficult to understand mathematically- it requires a certain level of dedication from the reader if the book is to be read back to back rather than act as a reference
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