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Fractional calculus and continuous-time finance

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Author Info

  • Enrico Scalas

    (Universita' del Piemonte Orientale, Alessandria, Italy)

  • Rudolf Gorenflo

    (Freie Universitaet Berlin, Berlin, Germany)

  • Francesco Mainardi

    (Universita' di Bologna, Bologna, Italy)

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://128.118.178.162/eps/fin/papers/0411/0411007.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0411007.

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Length: 11 pages
Date of creation: 05 Nov 2004
Date of revision:
Handle: RePEc:wpa:wuwpfi:0411007

Note: Type of Document - pdf; pages: 11. Preprint pdf version of a paper published in Physica A, vol.284, p.376-384, 2000.
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Web page: http://128.118.178.162

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Keywords: Stochastic processes; random walk; statistical finance; duration;

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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, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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