The traditional assumption that stock price changes could in theory be forecast by sufficiently detailed analysis of previous price fluctuations has only recently been found to have little empirical support when examined statistically. Some investigators now conclude that stock price changes are best approximated by classical Brownian motion.
More than sixty years ago, in 1900, a French student of economics, Louis Bachelier, in submitting a doctoral dissertation to Poincaré (Théorie de La Spéculation), proposed the notion that stock price changes are independent of all prior fluctuation. Never before published in English and barely known, the Bachelier study had been regulated to obscurity. It now recovers rightful place, being published in this volume along with the basic collection of current and more sophisticated work on stochastic processes.
Nearly all of the widely scattered, fundamental studies applying probability theory and a modern statistical approach to the problem of the predictability of stock prices are gathered in this volume: they report researches on (a) cases of random walks with increments that are independent Pareto-Levy variables, (b) non-linear random processes, (c) distributions of the range of sums of random variables, (d) spectral analysis, and (e) statistical estimation of Markov processes. Another major group of papers considers the implications of the theory of Brownian motion for the behavior of those prices that are related to stock prices: for example, puts and calls, warrants, and convertible bonds.
