“New Methods of Statistical Economics,” revisited: Short versus long tails and Gaussian versus power-law distributions



The standard “Brownian” model of competitive markets asserts that the increments of price (or of its logarithm) are statistically independent and Gaussian, implying that price itself is a continuous function of time. This model arose in 1900, at an immediately high level of perfection, in the work of L. Bachelier. In many fields of science it became a classic. But for financial prices it is sharply—even overwhelmingly—contradicted by conspicuous and strong symptoms of non-independence, nonGaussianity, and discontinuity. Since 1963, the author has been tackling those symptoms one by one: first, by incorporating strongly non-Gaussian marginal distributions (1963), then by incorporating strong long-term dependence (1965), and finally by combining those two features by introducing the new notion of multifractality (1968 and since). The goal of this article is modest: largely borrowing from the author's previous articles and books, much of it collects and adapts a few brief “teasers” or “appetizers” meant to promote and assist the future development of a framework for a realistic description of actual financial fluctuations. © 2008 Wiley Periodicals, Inc. Complexity, 2009