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Moment generating function of non-Markov self-excited claims processes

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  • Hainaut, Donatien

Abstract

This article establishes the moment generating function (mgf) of self-excited claim processes with memory functions that admit a Fourier's transform representation. In this case, the claim and intensity processes may be reformulated as an infinite dimensional Markov processes in the complex plane. Approaching these processes by discretization and next considering the limit allows us to find their moment generating function. We illustrate the article by fitting non-Markov self-excited processes to the time-series of cyber-attacks targeting medical and other services, in the US from 2014 to 2018.

Suggested Citation

  • Hainaut, Donatien, 2021. "Moment generating function of non-Markov self-excited claims processes," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 406-424.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pb:p:406-424
    DOI: 10.1016/j.insmatheco.2021.08.013
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    References listed on IDEAS

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    Cited by:

    1. Dupret, Jean-Loup & Hainaut, Donatien, 2022. "A subdiffusive stochastic volatility jump model," LIDAM Discussion Papers ISBA 2022001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Hainaut, Donatien, 2023. "A mutually exciting rough jump diffusion for financial modelling," LIDAM Discussion Papers ISBA 2023011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Hainaut, Donatien, 2022. "Pricing of spread and exchange options in a rough jump-diffusion market," LIDAM Discussion Papers ISBA 2022012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Hainaut, Donatien, 2022. "Multivariate claim processes with rough intensities: Properties and estimation," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 269-287.
    5. Leunga Njike, Charles Guy & Hainaut, Donatien, 2024. "Affine Heston model style with self-exciting jumps and long memory," LIDAM Discussion Papers ISBA 2024001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Hainaut, Donatien, 2022. "Multivariate rough claim processes: properties and estimation," LIDAM Discussion Papers ISBA 2022002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Hainaut, Donatien & Chen, Maggie & Scalas, Enrico, 2023. "The rough Hawkes process," LIDAM Discussion Papers ISBA 2023007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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    More about this item

    Keywords

    Self-excited process; Shot noise process; Hawkes process; Compound Poisson; Contagion;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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