• risk;
  • the starkly non-Brownian character of competitive prices;
  • new models for mild versus wild statistical variability


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