Brownian Motion: Basic Concepts

Abstract

Brownian motion is a key concept in economics in two respects. It underlies an important part of stochastic finance, which includes the pricing of risky assets, such as stock prices, bonds and exchange rates. For example a central model for the price of a risky asset is that of geometric Brownian motion (see Chapter 7). It also plays a key role in econometrics, especially in the distribution theory underlying test statistics for a unit root. For example, the limiting distribution of the familiar Dickey-Fuller pseudo-t test for a unit root is a functional of Brownian motion.