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Ambit Processes and Stochastic Partial Differential Equations

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • Ole E. Barndorff-Nielsen

    (Aarhus University, Thiele Center, Department of Mathematical Sciences and CREATES, School of Economics and Management)

  • Fred Espen Benth

    (University of Oslo, Centre of Mathematics for Applications
    University of Agder, Faculty of Economics)

  • Almut E. D. Veraart

    (Aarhus University, CREATES, School of Economics and Management)

Abstract

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis.

Suggested Citation

  • Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2011. "Ambit Processes and Stochastic Partial Differential Equations," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 35-74, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_2
    DOI: 10.1007/978-3-642-18412-3_2
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    Cited by:

    1. is not listed on IDEAS
    2. Fred Espen Benth & Paul Kruhner, 2014. "Derivatives pricing in energy markets: an infinite dimensional approach," Papers 1412.7943, arXiv.org.
    3. Fred Espen Benth & Heidar Eyjolfsson, 2015. "Representation and approximation of ambit fields in Hilbert space," Papers 1509.08272, arXiv.org.
    4. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    5. Ole E. Barndorff-Nielsen, 2016. "Assessing Gamma kernels and BSS/LSS processes," CREATES Research Papers 2016-09, Department of Economics and Business Economics, Aarhus University.
    6. Fred Espen Benth & Heidar Eyjolfsson, 2016. "Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations," Papers 1602.02907, arXiv.org.
    7. Pakkanen, Mikko S., 2014. "Limit theorems for power variations of ambit fields driven by white noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1942-1973.

    More about this item

    Keywords

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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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