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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 6: Poster Session

SOE 6.7: Poster

Montag, 31. März 2014, 18:00–20:00, P2

Modeling long-range dependent inverse cubic distributions by nonlinear stochastic differential equations — •Bronislovas Kaulakys, Miglius Alaburda, and Julius Ruseckas — Institute of Theoretical Physics and Astronomy, Vilnius University, A. Gostauto 12, LT-01108 Vilnius, Lithuania

One of stylized facts emerging from statistical analysis of financial markets is the inverse cubic law for the cumulative distribution of number of events of trades, volatility and of the logarithmic price change. Here we model the long-range dependent inverse cubic cumulative distributions by square multiplicative stochastic differential equations [1] and taking into account a transition from Stratonovich to Ito convention in noisy systems [2] according to Wong-Zakai theorem [3], with decrease of the driving noise correlation time when the market proceeds from turbulent to calm behavior.

[1] B. Kaulakys and M. Alaburda, J. Stat. Mech. P02051 (2009); J. Ruseckas and B. Kaulakys, Phys. Rev. E 81, 031105 (2010).

[2] G. Pesce et al, Nature Commun. 4, 3733 (2013).

[3] E. Wong and M. Zakai, Ann. Math. Stat. 36, 1560 (1965).