Multifractality is ubiquitously observed in complex natural and socioeconomic systems.
Multifractal analysis provides powerful tools to understand the complex nonlinear nature of …

Typically, complex systems are natural or social systems which consist of a large number of
nonlinearly interacting elements. These systems are open, they interchange information or …

In finance, one usually deals not with prices but with growth rates R, defined as the
difference in logarithm between two consecutive prices. Here we consider not the trading …

Publisher Summary This chapter discusses the new approach to the classic problem of
tâtonnement—the dynamic process through which markets seek to reach equilibrium. The …

We introduce a measure of activity of financial markets that provides a direct access to their
level of endogeneity. This measure quantifies how much of price changes is due to …

Complex systems consist of many interacting elements which participate in some dynamical
process. The activity of various elements is often different and the fluctuation in the activity of …

In this review article we present some of achievements of econophysics and sociophysics
which appear to us the most significant. We briefly explain what their roles are in building of …

This review deals with several microscopic ('agent-based') models of financial markets
which have been studied by economists and physicists over the last decade: Kim …

This paper reviews some applications of continuous time random walks (CTRWs) to Finance
and Economics. It is divided into two parts. The first part deals with the connection between …

Quantitative finance has had a long tradition of a bottom-up approach to complex systems
inference via multi-agent systems (MAS). These statistical tools are based on modelling …