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

Donatien Hainaut ()
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2021028, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: self-excited process; shot noise process; Hawkes process (search for similar items in EconPapers)
JEL-codes: C5 G22 (search for similar items in EconPapers)
Pages: 28
Date: 2021-07-02
New Economics Papers: this item is included in nep-ets, nep-isf and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2021028

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