Model for interevent times with long tails and multifractality in human communications: An application to financial trading

Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

Propagation through fractal media: The Sierpinski gasket and the Koch curve

We present new analytical tools able to predict the averaged behavior of fronts spreading through self-similar spatial systems starting from reaction-diffusion equations. The averaged speed for these fronts is predicted and compared with the predictions from a more general equation (proposed in a previous work of ours) and simulations. We focus here on two fractals, the Sierpinski gasket (SG) and the Koch curve (KC), for two reasons, i.e. i) they are widely known structures and ii) they are deterministic fractals, so the analytical study of them turns out to be more intuitive. These structures, despite their simplicity, let us observe several characteristics of fractal fronts. Finally, we discuss the usefulness and limitations of our approa

Imperfectly informed voters and strategic extremism

We analyze a unidimensional model of two-candidate electoral competition where voters have im- perfect information about the candidates' policy proposals, that is, voters cannot observe the exact policy proposals of the candidates but only which candidate offers the most leftist/rightist platform. We assume that candidates are purely office motivated and that one candidate enjoys a valence advan- tage over the other. We characterize the unique Sequential Equilibrium in very-weakly undominated strategies of the game. In this equilibrium the behavior of the two candidates tends to maximum extremism, due to the voters' lack of information. But it may converge or diverge depending on the size of the advantage. For small values of the advantage candidates converge to the extreme policy most preferred by the median and for large values of the advantage candidates strategies diverge: each candidate specializes in a different extreme policy. These results are robust to the introduction of a proportion of well informed voters. In this case the degree of extremism decreases when the voters become more informed.