Modeling the inverse cubic distributions by nonlinear stochastic differential equations

Author

Kaulakys, Bronislovas ; Alaburda, Miglius

Author_Institution

Inst. of Theor. Phys. & Astron., Vilnius Univ., Vilnius, Lithuania

fYear

2011

fDate

12-16 June 2011

Firstpage

499

Lastpage

502

Abstract

One of stylized facts emerging from statistical analysis of financial markets is the inverse cubic law for the cumulative distribution of a number of events of trades and of the logarithmic price change. A simple model, based on the point process model of 1/f noise, generating the long-range processes with the inverse cubic cumulative distribution is proposed and analyzed. Main assumptions of the model are proportional to the process intensity, 1/τ(t), stochasticity of large interevent time τ(t) and the Brownian motion of small interevent time.

Keywords

Brownian motion; econophysics; nonlinear differential equations; statistical analysis; stochastic processes; Brownian motion; financial markets; interevent time; inverse cubic cumulative distribution; inverse cubic law; logarithmic price change; nonlinear stochastic differential equations; point process model; process intensity; statistical analysis; stochasticity; Analytical models; Differential equations; Equations; Mathematical model; Noise; Steady-state; Stochastic processes;

fLanguage

English

Publisher

ieee

Conference_Titel

Noise and Fluctuations (ICNF), 2011 21st International Conference on

Conference_Location

Toronto, ON

Print_ISBN

978-1-4577-0189-4

Type

conf

DOI

10.1109/ICNF.2011.5994380

Filename

5994380