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Subdynamics of financial data from fractional Fokker-Planck equation

Janczura, Joanna and Wyłomańska, Agnieszka (2009): Subdynamics of financial data from fractional Fokker-Planck equation. Published in: Acta Physica Polonica B , Vol. 40, No. 5 (2009): pp. 1341-1351.

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Abstract

In exhibition of many real market data we observe characteristic traps. This behavior is especially noticeable for processes corresponding to stock prices. Till now, such economic systems were analyzed in the following manner: before the further investigation trap-data were removed or omitted and then the conventional methods used. Unfortunately, for many observations this approach seems not to be reasonable therefore we propose an alternative approach based on the subdiffusion models that demonstrate such characteristic behavior and their corresponding probability density function (pdf) is described by the fractional Fokker-Planck equation. In this paper we model market data using subdiffusion with a constant force. We demonstrate properties of the considered systems and propose estimation methods.

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