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...

The limit order book is a device for storing demand and effecting trades that is the primary mechanism for price formation in most modern financial markets. We study the limit order book under a random process model of order flow, using simulations and an analytic treatment based on a master...

Highly optimized tolerance is a model of optimization in engineered systems, which gives rise to power-law distributions of failure events in such systems. The archetypal example is the highly optimized forest fire model. Here we give an analytic solution for this model which explains the origin...

A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price formation to study the price dynamics induced by several...

We investigate the problem of learning to play a generalized rock-paper-scissors game. Each player attempts to improve her average score by adjusting the frequency of the three possible responses. For the zero-sum case the learning process displays Hamiltonian chaos. The learning trajectory can...

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,...

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks such as the Internet, social networks or biological...

We are interested in the strategic implications of asymmetric competition. Previous work (Carpenter, Cooper, Hanssens and Midgley [CCHM] 1988) has estimated the Nash-equilibrium prices and advertising expenditures for asymmetric market-share models in the extreme cases of no competitive reaction...

Experimentally it has been found that any two people in the world, chosen at random, are connected to one another by a short chain of intermediate acquaintances, of typical lenth about six. This phenomenon, colloquially referred to as the "six degrees of separation", has been the subject of a...

During the development of a multicellular organism for a zygote, a large number of epigenetic interactions take place on every level of suborganismal organization. This raises the possibility that the system of epigenetic interactions may compensate or ÒbufferÓ some of the changes that occur...