2000/01/10 by Enrico Scalas, Rudolf Gorenflo, Francesco Mainardi · 4 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Calculus (dental) #Character (mathematics) #Complex Systems and Time Series Analysis #Computer science #Diffusion #Economics #Finance #Financial Risk and Volatility Modeling #Financial market #Fractional Differential Equations Solutions #Markov process #Mathematical economics #Mathematics #Physics #Scaling #Series (stratigraphy) #Statistical physics #Statistics #cond-mat.dis-nn #q-fin.ST
paper · pdf · doi:10.1016/s0378-4371(00)00255-7
11 pages, no figures, LaTeX2e, submitted to Physica A
arxiv created 2000/01/10 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05
In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predictions on the long-time behaviour of the waiting-time probability density are presented. Finally, a general scaling form is given, based on the solution of the fractional diffusion equation.