In the present work we demonstrate the application of different physical methods to high-frequency or tick-bytick
financial time series data. In particular, we calculate the Hurst exponent and inverse statistics for the price
time series taken from a range of futures indices. Additionally, we show that in a limit order book the relaxation
times of an imbalanced book state with more demand or supply can be described by stretched exponential laws
analogous to those seen in many physical systems.
We extend to the multi-asset case the framework of a discrete time model of a single asset financial market
developed in Ghoulmié et al.<sup>1</sup> In particular, we focus on adaptive agents with threshold behavior allocating
their resources among two assets. We explore numerically the effect of this diversification as an additional source
of complexity in the financial market and we discuss its destabilizing role. We also point out the relevance of
these studies for financial decision making.
In the past few years, several studies have explored the topology of interactions in different complex systems. Areas of investigation span from biology to engineering, physics and the social sciences. Although having different microscopic dynamics, the results demonstrate that most systems under consideration tend to self-organize into structures that share common features. In particular, the networks of interaction are characterized by a power
law distribution, P(k)~ k-α, in the number of connections per node, k, over several orders of magnitude. Networks that fulfill this propriety of scale-invariance are referred to as "scale-free". In the present work we explore the implication of scale-free topologies in the antiferromagnetic (AF) Ising model and in a stochastic
model of opinion formation. In the first case we show that the implicit disorder and frustration lead to a spinglass phase transition not observed for the AF Ising model on standard lattices. We further illustrate that the opinion formation model produces a coherent, turbulent-like dynamics for a certain range of parameters. The influence, of random or targeted exclusion of nodes is studied.