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Fractional Calculus and Applied Analysis

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Volume 17, Issue 2


Fractional Skellam processes with applications to finance

Alexander Kerss / Nikolai Leonenko / Alla Sikorskii
  • Department of Statistics and Probability, Michigan State University, 619 Red Cedar Road, East Lansing, MI, 48824, USA
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Published Online: 2014-03-21 | DOI: https://doi.org/10.2478/s13540-014-0184-2


The recent literature on high frequency financial data includes models that use the difference of two Poisson processes, and incorporate a Skellam distribution for forward prices. The exponential distribution of inter-arrival times in these models is not always supported by data. Fractional generalization of Poisson process, or fractional Poisson process, overcomes this limitation and has Mittag-Leffler distribution of inter-arrival times. This paper defines fractional Skellam processes via the time changes in Poisson and Skellam processes by an inverse of a standard stable subordinator. An application to high frequency financial data set is provided to illustrate the advantages of models based on fractional Skellam processes.

MSC: Primary 60E05, 60G22; Secondary 60G51, 26A33

Keywords: fractional Poisson process; fractional Skellam process; Mittag-Leffler distribution; high frequency financial data

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About the article

Published Online: 2014-03-21

Published in Print: 2014-06-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 17, Issue 2, Pages 532–551, ISSN (Online) 1314-2224, DOI: https://doi.org/10.2478/s13540-014-0184-2.

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© 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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