Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ‘‘phantom traffic jams’ ’ even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ‘‘freeze by heating’’? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well. CONTENTS

We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.

The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns nonextensive systems, where nonextensivity is understood in the thermodynamical sense. This generalization was first proposed in 1988 inspired by the probabilistic description of multifractal geometries, and has been intensively studied during this decade. In the present effort, after introducing some historical background, we briefly describe the formalism, and then exhibit the present status in what concerns theoretical, experimental and computational evidences and connections, as well as some perspectives for the future. In addition to these, here and there we point out various (possibly!) relevant questions, whose answer would certainly clarify our current understanding of the foundations of statistical mechanics and its thermodynamical implications. I.

Abstract. This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Hölder singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically selfsimilar measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes. 1.

Introduction Since the 1980s, the deterioration of the academic job market in physics has been attracting a large number of physicists to investment banks: many of them are now working as \quants", designing sophisticated new derivative products or developing numerically intensive data analysis techniques for price and volatility forecasting. More recently, several teams of physicists have launched their own rms, oering services in the elds of nancial software design and forecasting. There exists however another set of motivations { scientic ones { which have also been prompting theoretical physicists { especially those with a background in statistical physics { to become interested in nance. Although this phenomenon may seem a bit mysterious to the outsider, we will attempt to convince the reader that it is not: nancial markets may well be considered as objects of high potential interest for researchers in statistical physics. 1.1 Motivations Statist

This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple trading strategies, and their trades together determine the stock prices. Computer simulations show that a basic case of this model is already capable of generating price graphs which are visually similar to the recent price movements of high tech stocks. In the general model, we prove that if there are a large number of traders but they employ a relatively small number of strategies, then there is a polynomial-time algorithm for predicting future price movements with high accuracy. On the other hand, if the number of strategies is large, market prediction becomes complete in two new computational complexity classes CPP and BCPP, where P NP[O(log n)] BCPP CPP = PP. These computational completeness results open up a novel possibility that the price graph of an actual stock could be suciently deterministic for various prediction goals but appear random to all polynomial-time prediction algorithms. 1

This paper investigates new properties concerning the multifractal structure of a class of random self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Hölder singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes.

We consider a class of microeconomic models with interacting agents which replicate the main properties of asset prices time series: non-linearities in levels and common degree of long-memory in the volatilities and co-volatilities of multivariate time series. For these models, long-range dependence in asset price volatility is the consequence of swings in opinions and herding behavior of market participants, which generate switches in the heteroskedastic structure of asset prices. Thus, the observed long-memory in asset prices volatility might be the outcome of a change{point in the conditional variance process, a conclusion supported by a wavelet analysis of the volatility series. This explains why volatility processes share only the properties of the second moments of long-memory processes, but not the properties of the first moments.

The Pareto (power-law) wealth distribution, which is empirically observed in many countries, implies rather extreme wealth inequality. For instance, in the U.S. the top 1% of the population holds about 40% of the total wealth. What is the source of this inequality? The answer to this question has profound political, social, and philosophical implications. We show that the Pareto wealth distribution is a robust consequence of a fundamental property of the capital investment process: it is a stochastic multiplicative process. Moreover, the Pareto distribution implies that inequality is driven primarily by chance, rather than by differential investment ability. This result is closely related to the concept of market efficiency, and may have direct implications regarding the economic role and social desirability of wealth inequality. We also show that the Pareto wealth distribution may explain the Lvy distribution of stock returns, which has puzzled researchers for many years. Thus, the Pareto wealth distribution, market efficiency, and the Lvy distribution of stock returns are all closely linked.

We address a current question in econophysics: Are fluctuations in economic indices correlated? To this end, we analyze 1-minute data on a stock index, the Standard and Poor index of the 500 largest stocks. We extend the 6-year data base studied by Mantegna and Stanley by including the 13 years 1984--1996 inclusive, with a recording frequency of 15 seconds. The total number of data points in this 13 years period exceed 4.5 million, which allows for a very detailed statistical analysis. We find that the fluctuations in the volatility are correlated, and that the correlations are well described by a power law. We also briefly describe some recent scaling results in economics, specifically some surprising features that appear to be common to the growth rates of business firms, countries, research budgets, and bird populations. 1999 Elsevier Science B.V. All rights reserved.