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Multivariate Self-Exciting Processes with Dependencies

Author

Listed:
  • Caroline Hillairet

    (CREST)

  • Thomas Peyrat

    (CREST)

  • Anthony R'eveillac

    (INSA Toulouse, IMT, UT)

Abstract

This paper introduces the class of multidimensional self-exciting processes with dependencies (MSPD), which is a unifying writing for a large class of processes: counting, loss, intensity, and also shifted processes. The framework takes into account dynamic dependencies between the frequency and the severity components of the risk, and therefore induces theoretical challenges in the computations of risk valuations. We present a general method for calculating different quantities related to these MSPDs, which combines the Poisson imbedding, the pseudo-chaotic expansion and Malliavin calculus. The methodology is illustrated for the computation of explicit general correlation formula.

Suggested Citation

  • Caroline Hillairet & Thomas Peyrat & Anthony R'eveillac, 2025. "Multivariate Self-Exciting Processes with Dependencies," Papers 2503.15958, arXiv.org, revised Mar 2025.
    • Handle: RePEc:arx:papers:2503.15958
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    References listed on IDEAS

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    1. Bessy-Roland, Yannick & Boumezoued, Alexandre & Hillairet, Caroline, 2021. "Multivariate Hawkes process for cyber insurance," Annals of Actuarial Science, Cambridge University Press, vol. 15(1), pages 14-39, March.
    2. Adrian Baldwin & Iffat Gheyas & Christos Ioannidis & David Pym & Julian Williams, 2017. "Contagion in cyber security attacks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 780-791, July.
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