In financial markets an excess of buying tends to drive prices up, and an excess of selling tends to drive them down. This is called market impact. Based on a simplified model for market making, it is possible to derive a unique functional form for market impact. This can be used to formulate a...

Physicists have recently begun doing research in finance, and even though this movement is less than five years old, interesting and useful contributions have already emerged. This article reviews these developments in four areas, including empirical statistical properties of prices,...

We use game theory and the Santa Fe Artificial Stock Market, an agent-based model of an evolving stock market, to study the properties of strategic Nash equilibria in financial markets. We discover two things: there is a unique strategic equilibrium in the market, and this equilibrium in...

In this review article, we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate...