The random walk model in finance.

Summary The backbone of the modeling of stock market variations, the random walk model has known different mathematical forms during its eventful history. This book presents this model in a systematic way, from its intuition in the mid-19th century to its most recent transformations. It describes the origins of the idea of random walk in finance, the statistical validation and intellectual domination of this model in professional practices, and provides an overview of the scientific controversies that have accompanied it since its birth. Several specific aspects are discussed: the interaction between the random walk model and the hypothesis of market efficiency, the relationship between the normal law and modern portfolio management, the influence of the Brownian representation on the notion of perfect hedging of options, and the change in time frame with the introduction of intrinsic stock market time. The persistence of this model, while many problems remain, is analyzed in the context of contemporary debates around techno-sciences. [4th cover].