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Fractional calculus and continuous-time finance

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Author Info

  • Scalas, Enrico
  • Gorenflo, Rudolf
  • Mainardi, Francesco

Abstract

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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0378437100002557
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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 284 (2000)
Issue (Month): 1 ()
Pages: 376-384

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Handle: RePEc:eee:phsmap:v:284:y:2000:i:1:p:376-384

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Stochastic processes; Random walk; Statistical finance; Econophysics;

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  1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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