We demonstrate that continuous-time FARIMA processes with α-stable noise provide a new stochastic tool for studying the solar flare phenomenon in the framework of fractional Langevin equation. Simple computer tests to check the origins of α-stability and self-similarity are implemented for...

We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency...

We show that intrinsically random dynamical systems with the Prigogine operator Λ of the form of a random Laplace transform, can be characterized as Kolmogorov flows (K-flows). We also obtain a spectral characterization in the language of the Weyl commutation relation. As a consequence we...

The conditionally exponential decay (CED) model is used to explain the scaling laws observed in financial data. This approach enables us to identify the distributions of currency exchange rate or economic indices returns (changes) corresponding to the empirical scaling laws. This is illustrated...

In this paper we show that the logarithmic returns of the Hang Seng index from January 2, 1987 to November 14, 2005 statistically resemble a sequence of independent identically distributed Lévy stable random variables. This is in stark contrast to Xiu and Jin (2007) [39], where long-memory...

Property claim services (PCS) provides indices for losses resulting from catastrophic events in the US. In this paper, we study these indices and take a closer look at distributions underlying insurance claims. Surprisingly, the lognormal distribution seems to give a better fit than the Paretian...