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Population viewpoint on Hawkes processes

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  • Alexandre Boumezoued

Abstract

This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of age pyramid which evolves according to immigration and births. The virtue if this approach that combines an intensity process definition and a branching representation is that the population age pyramid keeps track of all past events. This is used to compute new distribution properties for a class of linear Hawkes processes with general immigrants which generalize the popular exponential fertility function. The pathwise construction of the Hawkes process and its underlying population is also given.

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  • Alexandre Boumezoued, 2015. "Population viewpoint on Hawkes processes," Papers 1504.06563, arXiv.org.
    • Handle: RePEc:arx:papers:1504.06563
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    File URL: http://arxiv.org/pdf/1504.06563
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    References listed on IDEAS

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    1. A. Saichev & D. Sornette, 2011. "Generating functions and stability study of multivariate self-excited epidemic processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 83(2), pages 271-282, September.
    2. Spencer WHEATLEY & Vladimir FILIMONOV & Didier SORNETTE, 2014. "Estimation of the Hawkes Process with Renewal Immigration Using the EM Algorithm," Swiss Finance Institute Research Paper Series 14-53, Swiss Finance Institute.
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    Cited by:

    1. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.

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