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Steele JM (2001) Stochastic Calculus and Financial Applications. Springer, New York - Berlin - Heidelberg, ix + 300 pp., US $ 79.95, ISBN 0-387-95016-8.
Ten years ago there were only a few texts on stochastic calculus with applications to finance. Meanwhile there are new textbooks every other month, from elementary introductions written for students of business administration to advanced texts requiring a strong background in stochastic processes and functional analysis. The book under review is an intermediate text, in the sense that although it requires some previous exposure to probability and statistics and makes no compromises in terms of rigor, it does not aim at "the general case." This means, among other things, that the stochastic integral is developed for Brownian motion only, general semimartingales do not appear. Instead, as Steele explains in the preface, "this is a text with an attitude," being designed to reflect "a prejudice for the concrete over the abstract."
The first chapter presents the random walk and some aspects of...