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Ambit Processes, Their Volatility Determination and Their Applications

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Modern Stochastics and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 90))

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Abstract

In this chapter we try to review the research done so far about ambit processes and their applications. The notion of ambit process was introduced by Barndorff-Nielsen and Schmiegel in 2007. Since then, many papers have been written studying their properties and applying them to model different natural or economic phenomena. As it is shown in the paper, these processes share their mathematical structure with the solutions of random evolution equations allowing them great flexibility for modelling. The goal of this paper is fourfold: to show the main characteristics of these processes; how to determine their main structural component: their volatility; how they can be used for modelling different random phenomena like turbulence or financial prices; and last but not least the mathematics behind.

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Authors and Affiliations

  1. University of Barcelona, Gran Via Corts Catalanes 585, 08007, Barcelona, Spain

    José Manuel Corcuera, Gergely Farkas & Arturo Valdivia

Authors
  1. José Manuel Corcuera
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  2. Gergely Farkas
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  3. Arturo Valdivia
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Corresponding author

Correspondence to José Manuel Corcuera .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Volodymyr Korolyuk

  2. Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, Compiegne Cedex, France

    Nikolaos Limnios

  3. Dept. of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Yuliya Mishura

  4. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Lyudmyla Sakhno

  5. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Georgiy Shevchenko

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Corcuera, J.M., Farkas, G., Valdivia, A. (2014). Ambit Processes, Their Volatility Determination and Their Applications. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_14

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