Author J. Steele.
Publisher New York: Springer-Verlag, 2000, pp. x + 300, US$ 69.95/DM154.95.

Readership: Anyone with an interest in probability and finance, university level mathematics and probability theory

This is a world of "lovely exercises" that are "very good for the soul", "honest martingales", "bedrock approximations", portfolios that are "born to lose", "intuitive but bogus arguments", and "embarrassingly crude insights". In short, this is a book on stochastic calculus of a different flavour. Intuition is not sacrificed for rigour nor rigour for intuition. The main results are reinforced with simple special cases, and only when the intuitive foundations are laid does the author resort to the formalism of probability. The coverage is limited to the essentials but nevertheless includes topics that will catch the eye of experts (such as the wavelet construction of Brownian motion). This is one of the most interesting and easiest reads in the discipline; a gem of a book.

Institute University of Waterloo
Place Waterloo, Canada
Name D.L. McLeish