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Fractional calculus and continuous-time finance

Author

Listed:
  • 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.

Suggested Citation

  • Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA.
  • 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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    File URL: http://econwpa.repec.org/eps/fin/papers/0411/0411007.pdf
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    References listed on IDEAS

    as
    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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    Keywords

    Stochastic processes; random walk; statistical finance; duration;

    JEL classification:

    • G - Financial Economics

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