This is an important and useful text. Too often, analysts have swept everything under the rug of the Gaussian (i.e., Normal) distribution. It represents the victory of ease over analysis. Assuming the Normal distribution puts tables and easy computations of probability at hand. Mandelbrot presents evidence that taking the Normal curve as given in many cases when distributions have tails that follow power laws is to err seriously. In this regard, he presents a critique of much of modern finance that hinges on the Gaussian distribution.
In fact, one might argue that the real nature of the Black Swan problem is one of misspecification of the underlying probability distribution. If one reasonably assumes that one probability distribution holds, then an error in selection of that distribution can have significant consequences, especially at the extremes of the distribution. The Normal distribution, in particular, has quite thin tails: the probability of an event six standard deviations from the mean (the 6 sigma criterion) at 3 per million events is small beyond any plausibility. All that is guaranteed under Chebyshev's rule, however, is that the probability of an occurrence at that extreme in no more likely than about 3%. The difference represents an increase by 10,000 times in probability. What is assumed rare might, indeed, be disastrously common.
Unfortunately for this book, its author's personal problems and history detract from the text. He insists on reminding the reader that he was a pioneer in the field of fractal analysis. He revisits previous positions where he was denied tenure or a chair or recognition for his achievement. Dr. Mandelbrot's reputation is secure; he is not alone in having some of his best work overlooked. The repetition of these old hurts adds nothing to the text.
This book is recommended with some reservations.
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