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Fractional calculus and continuous-time finance

  • Enrico Scalas
  • Rudolf Gorenflo
  • Francesco Mainardi

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 L\'evy 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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Paper provided by in its series Papers with number cond-mat/0001120.

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Date of creation: Jan 2000
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Handle: RePEc:arx:papers:cond-mat/0001120
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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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