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Construction and Simulation of Generalized Multivariate Hawkes Processes

Author

Listed:
  • Tomasz R. Bielecki

    (Illinois Institute of Technology)

  • Jacek Jakubowski

    (University of Warsaw)

  • Mariusz Niewęgłowski

    (Warsaw University of Technology)

Abstract

The main contribution of the paper amounts to providing a mathematical construction of a generalized multivariate Hawkes process (GMHP), as well as a simulation algorithm based on this construction. In particular, we justify the construction by demonstrating that the constructed process is indeed a GMHP with desired properties. Towards this end we provide some new results regarding conditional Poisson random measures and doubly stochastic marked Poisson processes.

Suggested Citation

  • Tomasz R. Bielecki & Jacek Jakubowski & Mariusz Niewęgłowski, 2022. "Construction and Simulation of Generalized Multivariate Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2865-2896, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09934-5
    DOI: 10.1007/s11009-022-09934-5
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    References listed on IDEAS

    as
    1. Dassios, Angelos & Zhao, Hongbiao, 2013. "Exact simulation of Hawkes process with exponentially decaying intensity," LSE Research Online Documents on Economics 51370, London School of Economics and Political Science, LSE Library.
    2. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    3. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    4. Jesper Møller & Jakob G. Rasmussen, 2006. "Approximate Simulation of Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 53-64, March.
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